to strive is:
1. to try or work hard
2. for the purpose of asserting of oneself
so, there is NO intrinsic meaning of "opposing" in the word "strive".
that is why "strive" is typically used in a positive fashion.
I strive for personal independence - this does not mean I fight with my parents.
He strives for career success - this does not mean that he plays office politics.
Of course, in the process of asserting oneself, conflict is likely to occur.
So, there might be some hints on physical and psychological conflicts.
Nonetheless, you should picture the positive "hard word" more than the "conflicts" from this word.
Back to your original question:
to strive for verbal resolution
= to work hard in conscience rhetoric agreement
= to (work hard to) assert myself in rhetoric
but not 以德服人