End Game Theory

Based on my experience with kdramas - if the leads were not meant to be together, they wouldn't have revealed Kim's name so early on. They would've mentioned the father without naming him so that people assume that ML is the father and then closer to the finale BAM it would've been revealed that the father is someone else. (Remember Reply 1988 which showed the husband without clarifying who he was) However, the opposite has happened here, they revealed that the father is Kim from the very beginning in a deliberate attempt to make people believe that the leads won't end up together. Dramas usually don't do that if the leads are actually not meant to be together. In order to maintain suspense wrt the ending, the beginning is always misleading. The FL seems to have a stable marriage in the future so that negates the ending theory that the daughter will help reunite the leads - this drama will not break a marriage just to bring the leads together and the daughter will definitely not root for the couple of her father is someone else. 

A small observation from the latest episode to support the dementia theory - I am one of the people who didn't like the scene between heedo's mom and daughter about her mom's coverage about the "stolen gold medal". (I understand people are arguing that it was her job, but I would argue that it was simply bad journalism - a discussion for another day). However, another perspective would be that the daughter knows about her grandma's condition and that's why she gave a biased view to appease her. In that scene she showed more maturity than she has done in all her scenes with her mom, maybe because she knows she is sick? Even in the earlier episode when her grandma asked her if she knows yijin, she had a strange expression while saying no and even heedo had a strange expression when her mom was talking about meeting yijin last month. The grandmother is the common factor in all the conversations which make us believe that yijin is no longer in their lives. More importantly, she is being shown as a terrible mother (and friend), the dementia plot might be used as a redemption arc to make viewers feel bad for her. 

 OneAjhussi:

It is unlikely that Yi Jin is Hee Do's husband and Min Chae's father. 

Min Chae has seen many pictures of Yi Jin and she does not recognizes him as her dad. She is reading her mom's diary telling about him and it is not like she is  reading about her dad. Why her mom do not refer to  Yi Jin as her husband? If he was her father, she would have plenty of pictures of him in her house, of them three together or she would have had discussion with him about "How I met your mother".

If they turn this in a way that Yi Jin is her father who is abroad working but still can send her a gift when her grandmother said she has not seen Yi Jin for years, then they used the biggest stunt ever. 

That's why the perspective used during the cinematography of specific scenes is important. After the first few episodes, everybody believed that hee do was raising her as a single mother because they didn't show the father or even mention him but that was obviously proven wrong. Just because they did not show the family photos of the three of them does not mean that there are actually no photos of them in that house, it simply means that they haven't shown them yet. The PD is trying to maintain the suspense wrt the real father so of course they wouldn't show them having a clear conversation about the dad, that would ruin the suspense. So at this particular point of time, we can't say anything. He could be the father and he also could not be the father. 

But still, I would prefer it if maybe they just changed Min Chae's surname or maybe their father (Yi Jin and his bro's) changed his surname to start another company? I hoped somehow in the starting and even now that they would end up together. 

@Roro2022 

"The PD is trying to maintain the suspense wrt the real father"

To this point, if the father is Yi Jin, that would not be maintaining the suspense, it would be "leading on the audience"...

 Xie Lalisa The Lil Kid:

But still, I would prefer it if maybe they just changed Min Chae's surname or maybe their father (Yi Jin and his bro's) changed his surname to start another company? I hoped somehow in the starting and even now that they would end up together. 

I believe Hee Do and Yi Jin parted ways in a very painful way. This is why she never talked to her daughter about her past and her teen years and her former bf and her daughter has to learn everything from a diary. This is also why Hee Do and Yi Jin have never contacted each other for years to ment their relationship. I also feel old Hee Do has lost many of the good traits of her personality she had when she was a teen. She became quite a sad and bland person.

I feel a bit stung along by the way they are doing the present day story.

I mean there has to be a reason for Min Chae to learn about her mother's first love. I suppose just learning more about her mom during a time when her mom was working hard at her sport so it could related back to ballet is reason enough. But it feels hollow to me?

Either Hee Do and Yi Jin are together and all the plot holes will be filled.

Or they aren't and this is a story about losing your first love, which is realistic but depresssing. 

idk. the present day story is just frustrating me.

@Roro2022

Actually, I don't know if it's the actress or is it just me but when I watched the grandmother in previous episode she looks a little weird when she was smiling so lovingly to Min Chae, so maybe the dementia plot is not that far away from the truth? Lol. I don't know, it seems weird to have that storyline but the story has always been unpredictable.

You also said this which kinda make sense for me as well:
"The grandmother is the common factor in all the conversations which make us believe that yijin is no longer in their lives."

--

Anyway, I'm slowly accepting that maybe Yi Jin is really not Kim Min Chae's father and Hee Do and Yi Jin were soulmates but not lovers in the end. However, I do have some theories like

1. Min Chae is still Yi Jin and Hee Do's daughter. Hee Do got pregnant but both he and Yi Jin ended things mutually to support the dream of the other or family problem had occurred. Hee Do believes that Yi Jin deserves to be happy so she did not stop him wherever he was going and he's not aware of his daughter and Hee Do met a Mr. Kim and he accepted Min Chae as his daughter. I just couldn't give up the father and daughter mirror things posted in twitter! Lol.
2. They never dated and stayed friends. HOWEVER--very impossible because if they did stay as BBFs, why he's something that Min Chae doesn't remember? 
3. Hee Do is divorced and the daughter is to a Mr. Kim. She will meet Yi Jin again without the help of his daughter and there's an open-ending. However, I doubt that she is divorced. So the only possible ending here is that they reconciled and become supportive BFFs again. I honestly don't want this because I want them to be happy "together" and build their own family and I really hate the "right love at the wrong time" trope, though that is still possible, but please don't complicate many things and just fall in love. However, if this what this drama will give me, I guess I should accept T_T
4. Let's just turn a blind eye on the photo thing. Min Chae didn't immediately recognized his father and that the continuation of the conversation was cut. Min Chae learned that Baek is the then-surname of his father. Now, in the video scenario she doesn't really need to acknowledge that "Baek Yi Jin" is her father, because she doesn't use much honorary words with her parents.  She already knows that he is her father and that she already confirmed things.