Okay, to start, what is telepathy?
Simply put, it is the ability to transmit the electrical impulses from your brain to another person's through no apparent sensory means. Right?
Correct me if I'm wrong, but that would either mean said impulses teleport directly into their brain (which is pretty much impossible), or the impulses are escaping your brain, escaping your skull, flying through the air, somehow getting into the other person's brain, and organizing themselves into whatever you were thinking. And it's pretty much impossible for those impulses to travel much more than the length of a nerve cell, as evidenced by the fact that they need to repeat themselves at the end of every cell. Also, brain and nerve cells are way more conductive than the air, as evidenced by the fact that electricity actually follows these pathways. Electricity will always take the path of least resistance, so you can't really just command your electrical impulses to jump out of the pathways they would go in according to the laws of physics. Especially considering how you would be trying to command those impulses USING MORE IMPULSES.
It's theoretically possible to channel those impulses from your brain cells to your nerve cells, which could channel them to nerve endings just inside your skin, allowing them to jump to another person's nerve endings on contact. However, this would require vastly more complex nerve cells, which would require a few million or so more years of evolution.
So in summary, It's telepathy through contact is theoretically possible, but impossible given our current evolutionary point. Otherwise, it pretty much breaks the laws of both physics and logic.