“Why do you insist to find...,

[Silverobama]

My cousin broke up with his 15th girlfriend and he always told me the reason was because “They are not good-looking”. I asked him “Why do you insist to find a good-looking woman?” Is my italic sentence natural?

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[tedmc]

It is "insist on something (gerund)".
Did your cousin realise his girlfriends were not good looking only after going through the relationships?

 

[emsr2d2]

My cousin recently broke up with his 15th fifteenth girlfriend. and he always told Every time he goes through a break-up, he tells me the reason was because is “They are not good-looking”. I asked him “Why do you insist to find on finding a good-looking woman?”

Is my italic sentence natural?​

Note my corrections above. Honestly, the whole thing makes little sense. Most people need to find someone else at least passably attractive before they start dating them. As tedmc suggested, your cousin's statement makes it sound as if he dates them for a while and then, one day, suddenly thinks "Oh, you're not attractive" and dumps them. I simply don't believe that's what's happening. I'd be interested to know whether it's your cousin or the girlfriend who makes the decision to break up each time.
In this context, it would make more sense for you to ask "Why don't you try deciding whether they're attractive or not before dating them?"

 

[Silverobama]

I'd be interested to know whether it's your cousin or the girlfriend who makes the decision to break up each time.

Maybe it was his girlfriends who decided to break up with him. Thanks a lot for your explanations. If someone who thinks beauty is what he needs the most when it comes to finding a girlfriend, is it natural to say "Why is good-looking so important for you when you find a girlfirend?"

 

[emsr2d2]

Maybe it was his girlfriends who decided to break up with him.

I think that sounds quite likely!

Thanks a lot for your explanations.

You're welcome.

If someone who thinks beauty is what he needs the most when it comes to finding a girlfriend, is it natural to say ask him "Why is good-looking attractiveness so important for to you when you find looking for a girlfriend?"

See above.

 

[Skrej]

Is it a case that he doesn't find them attractive, or just not attractive enough (however he sets that standard)?

Either way, it still seems strange that he can't decide whether or not they meet his standards for physical beauty before dating.

Dating them and then deciding they're not attractive or attractive enough sounds more like he's looking for some kind of inner beauty or personality quality, not physical beauty. That would make more sense why it requires spending some time with them to decide on attractiveness.