I have heard two reasons for women being exempt from time-bound mitzvot and both seem problematic, so either there are additional explanations or I am not properly understanding these two:
Women have to spend time on maintaining the household and raising the children, so they do not have time for time-bound mitzvot. But if that's the reason, the rabbis could have said "those with child-care duties (etc) are exempt". As it stands, women with no children don't have the reason but are still excused, and men who have child-care duties are still obligated. (Granted that the rabbis of the talmud were probably not considering this latter case.) It seems odd to me that a stay-at-home dad is obligated while his teenage daughter is exempt.
Women are on a higher spiritual plane and do not need as many mitzvot. It seems surprising to me that we could make that kind of statement about all women (and the converse about all men). Just looking around at the people I've met, there are wise men who seem not to need extra help and women who struggle and might need the help of more mitzvot.
What am I failing to understand about these two reasons? Or are there others?