To meet (met is the past tense) means to be introduced to, or to come in contact with, to run into. "I met you at the park.", "I met you at the party." To meet with (met with is the past tense) means to stop for a while to discuss something, to have a meeting. "I met with you at the office to talk about work.", "I would like to meet with you to discuss music."

There is an inference suggested that such a speaker would rather meet with someone else. That is the key point.

Both are past tense. The "with" implies a grouping scheme. It has the same difference as saying "Those people" rather than "My people". Most apprehensive people not fluent with deductive reasoning will be oblivious that they are saying such. The process is called CORFing in psychology, Cutting Off Reflected Failure. The one whom says "I met with you" is pushing you aside.