"may" or "can"

Before I take the time to write you a free essay in response to your question here, please take the time yourself to state what you think the answers are to  your own questions here and why you think what you do.

@David, Moderator posted:

Before I take the time to write you a free essay in response to your question here, please take the time yourself to state what you think the answers are to  your own questions here and why you think what you do.

OK. What I think is:

a) Children of divorced parents can have difficulty with relationships.

is equivalent to: It is possible for children of divorced parents to have difficulty with relationships. That is, this is what is generally true/possible with "children of divorced parents."

This is a statement that might be said by someone who has experienced it in his/her own life, or seen others face it, or may have read or heard about it somewhere (that such children do have difficulty with relationships).

Although there is a possibility that there may be children of divorced parents who do not have difficulty with relationships, but the original statement with "can" does not indicate anything as such. It only suggests what is the case, and not what is not the case.

b) Children of divorced parents may have difficulty with relationships.

is equivalent to: It is possible that children of divorced parents have/will have difficulty with relationships, but it also suggests that there is a possibility that they do not/will not have difficulty with relationships.

As it stands, the statement with "may" is a little more specific, and is dependent upon certain conditions.

This is a statement that might be said by someone who has neither experienced it nor read or heard about it anywhere, but thinks that it is possible, although they aren't very sure of their statement.

c) For the above reasons, I think, "could" and "might" could replace "may" in sentence (1). ("could" and "might" are used in more specific situations than "can")