"He is that delicate-like--He gave his mother a new coat last Christmas--but he wouldn't think of giving me anything so personal-like."
What's the use of "delicate-like","personal-like"?
The "-like" after each word is unnecessary; it's just there to emphasize the speaking style of the character.
"He is that delicate-like that he gave his mother a new coat." Unlike some men, he has a compassionate, thoughtful side to his personality and he remembered his mom at Christmas and bought her a nice new coat.
"He wouldn't think of giving me anything so personal."
Clothing is often thought of as a personal gift - something you would only give to someone you know very well, someone who is very close to you. Apparently the man in this story wouldn't give his girlfriend a gift like that. It seems like the point she is trying to make is that he'll take the time and money to buy a nice new coat for his mother, but doesn't go to the same amount of trouble for his girlfriend, who feels that she should be just as close to him in his heart.