Is it normal it upset me that a Muslim wouldn't shake my hand?

Please if you want to understand Islam and that rule don't ever ask Shia ... they are so rude and their job is to make people away from the truth of islam.
I will tell you the thing behind that rule i did some search and look what i have found :
It has been scientifically proven that the surface of the human skin contains millions of cells that transmit sensations to the brain , if the man's hand touched the woman's hand began signals resulting from contact with applicable toward the brain where analyzed and linked with his or her hand. When this process is repeated , the brain stores this information drives the passion for men or women , leaving the psychological impact and emotions remain stored for long periods of time .

The psychological emotions concerning handshake for men and women versa may evolve and excite instincts inherent in both sexes , which pays for more emotional and emotions that may be the cause of the evolution of the relationship between the sexes , leading to falling into the outrageous. At the very least has caused repeated handshake between men and women and frequent mixing between them to confuse the mind and influenced the decision - making process on both sides.

Islam wants the believer to be net - minded in stable condition and comfort in the heart.
I hope that help you to understand more :D