not a teacher
I think "don't go to the heart of the matter" works alright here, but it might be more commonly expressed as "guys sometimes don't want to go to the heart of the matter". As your example implies, men are often considered to be reluctant to talk seriously about relationship problems, which is probably the point that's being made.
Your suggestion, "guys sometimes miss the point", could fit, but in this case it might have the implication that he genuinely doesn't see where the problem is, although it may be clear to his partner. So it depends on the situation.
The phrase "my second half" doesn't seem natural to me. People sometimes use "my other half" to mean their long-term partner, or in the case of married couples, "my better half".