I hate how often people argue about things with me and then they say that I must not understand what they're saying. That's a totally illogical conclusion to assume that just because someone disagrees with you, they must not understand you. That's simply based on the egotistical assumption that there is only one possible conclusion given the facts and that conclusion is yours. This has become a pet peeve of mine because so many people use it.
Think about the situation logically and you will see: There are several possible conclusions that can be drawn besides the possibility of the other person simply not understanding you.
1. The other person sees your reasoning but you don't see his.
2. Both people see both sides but simply come to a different conclusion due to personal values or whatever.
3. Neither person sees the other side's reasoning.
On top of this, even if you truly believe that the other person is simply not seeing your reasoning, it is terrible form to accuse them of it. It is insulting, since it implies they are dumber than you are. It points the finger of blame at them for having an argument at all. It is a step along the path toward the argument becoming unresolvable since you've now turned it personal instead of it remaining a debate of ideas.
So basically, never, ever accuse the other person of failing to see your reasoning. It accomplishes nothing. Instead, focus on what you can control, which is presenting your own reasoning more clearly and attempting to understand what is preventing the other person from understanding you and making sure you are understanding the other person.
Eventually, the only unresolvable argument is the second situation, in which case, you and the other person simply must coexist with differing opinions.