Why didn't her dad beg for support instead of giving her up?

Not saying that he’s completely faultless, but sometimes relinquishing custody of a child is for the best of both parties. Imagine if a parent decides to keep their child but can’t properly care for them or provide proper necessities. Stable housing, food, health care, etc. are all important things that some people struggle to provide for their children, and the lack of those things make huge impacts on a child’s development. Honestly, I understand where the dad is coming from, but if I were Jiu’s shoes, I wouldn’t want to give her up either. This is a tough one. :(

Forgot to add that sometimes, the responsible thing to do is knowing what your limits and capabilities are

I totally agree, there is nothing wrong with relinquishing custody If he is unable to care for the child.
But then he shouldn't expect to be able to take her away again when he feels like it's more convenient now.
That's messed up. Seems like it's more about his guilt rather than her wellbeing. Ripping her from her family AGAIN...

But he isn't taking her because is convenient, they literally say "now he can afford to take care of her" which is totally different to taking her because is convenient

I imagine that after losing his wife he was depressed, we don't know if he had an stable job and income or even if he had a house, remember that even dying is expensive

So, the thing here is, he was responsable enough to ask for help if he couldn't take care of her completely, it seems that he was also in contact with them, as the little girl knows he is her dad and it seems he tries to get updates from them often but it also seems that the updates he get are very short

He didn't even know that his brother-in-law is in a relationship, which isn't a problem but he didn't know that the girl was already seeing themselves as a family, like what could have happened if the dad arrived when she was testing them? Maybe she could have asked her dad to take her for a day or two just to keep teasing them and that could have been worse as he wouldn't know what's going on

Anyway we know that they will keep the child as it usually happens in the mangas, but my point is... the father doesn't look like an irresponsible and detached person

Like the only thing Yiu didn't like about her dad was his beard ╮(￣▽￣)╭

Did we read the same chapters? The father called and said " Hey, it's It's been a long time. " He also said to the guy at the airport "It's been so long since I've last seen her, so I hope she hasn't forgotten me." in Chapter 7.

Sounds to me like he never saw his daughter after 'giving' her to Jiu. Also the way he arrives, tries to hug Yui and talks to Jiu about custody but leaves immediately after is weird. He came to see his daughter he hasn't seen in a while but doesn't try to bond and just leaves?

And I didn't mean to get into this so deeply lol. I chose the word "convenient" because Jiu said "He couldn' t afford to raise her now he can provide her a life without worries" which sound off, might be a translation issue or whatever.

We can imagine he was depressed after his wives death but imagine what Yui must have felt loosing both parents. Because we can clearly see what this did to her. In this one chapter she gets really quite and sais "don't leave Yui behind".

And now her father wants exactly that.