While love is about giving your all, some characters do not deserve that love.

We see a lot of dramas where one of the two does whatever they want to do regardless or hurting or not the other person. The person does not have to love the other one, but the one giving their all should know when to respect themselves, and value themselves. 

When this happens, I enjoy when this person gets some distance, and if the selfish one goes through some kind of redemption arc and//or at least show regret, and chase after the other, I believe can be worth it.

"My Fated Boy" first episode is a perfect example of that. 

Two questions...

1. Is it because maybe the main target to some of these dramas are women that the writers allow the female lead to behave this way, and the one that has to come crawling is the male one even when the female was wrong?

2. Is this acceptable? 

This type of thing doesn't usually bother me in dramas, unless the person on the receiving end of the love is downright abusive or cruel. This doesn't apply to Lin Yang because she was always very clear in how she saw Lu Zheng An. In My Fated Boy, you find out throughout the drama that Lu Zheng An can see right through Lin Yang. He knows she has feelings for him even when she's in denial about it. In his case, he refuses to give up on her because he knows she just needs to acknowledge and understand the feelings she already has. I think if Lin Yang really didn't have feelings for Lu Zheng An, he would've moved on from her. We're dealing with a couple who literally grew up together, which is a very different type of relationship compared to a couple who met as adults.

I don't think a redemption arc for Lin Yang was needed. She didn't do anything wrong because she acted according to her feelings as she understood them. The only mistake she really made was taking so long to recognize the true nature of her feelings. As for everything Lu Zheng An did for her, she saw that as something he should be doing as her younger brother. She thought the way he treated her was appropriate for their "platonic" relationship. For me, Lin Yang redeemed herself by immediately confessing to Lu Zheng An when she realized her feelings were not platonic, instead of continuing to be in denial or leaving him hanging. I think Lin Yang's a truer repentance than the cartoonish kind of the reversed chasing we often see because she showed right away that she was not going to repeat the same mistake.

A lot of this is a matter of preference, though. I usually dislike the reverse chasing trope because it takes forever and I don't find it realistic at all. I really like the way My Fated Boy handled it, but not everyone does and that's ok. We're just bound to have different perspectives on what the problem is and different ways we would personally fix the problem.

I have not seen the full show and I'm stuck on episode 13, unsure of whether to drop it or continue. 

But I agree with the OP from what I've seen until now. One needs to value themselves, in any kind of relationship. Here, all along, I've not seen the ML value himself even once. Yes, making her realise her feelings is one thing, not giving up is fine and I don't find it to be problematic at all, but the way the FL just keeps on humiliating him, shouting at him, letting her insecurities get the better of her and lash out at him is too much and no one should tolerate that, especially under the garb of love. That's just plain abuse. 

Literally in Episode 11/12, she acknowledges the possibility of love and then again you see her being dominating and overbearing with the ML. Just because you can't deal with your feelings (coherent or incoherent) you do not get the right to take it out on anyone else. 

To each its own I guess, but it is putting me off enough for me to seriously consider dropping this show with a rating of 1 (just because I can't give it 0)!