I passed a turn since I don't really see the point in continuing and my opponent also passed. It turned out that a corner of the board turned out to be a seki. My opponent urged me to continue, yet I do not want to. I was winning at that time. He wasn't letting me go so I continued to play, losing for about .5 points. Would it be ill mannered for me to not continue play? Should I have not play? I don't know much yet things about go.

When both players passed, as they did in your scenario, the game is over and you should have scored it as it was at that point. You can (in Japanese rules, which you're probably using if playing is costing you points) demand to play out a dispute after both players passed, but you don't change the score by doing so--either put the stones back before you count, or use pass stones to cancel out the extra stones you played while you play out the dispute. Also, unrelated to your question, while you're playing out the dispute, if you want to take back a ko you have to pass for that ko, rather than just playing someplace else.