Being able to cancel training was a popular request because sometimes people would train the wrong pet or, more commonly, would train the wrong stat accidentally. It's better to have a way to cancel than no way at all in the case of a mistake. There's no need to worry about accidentally clicking, because if you do, you can simply click "Cancel" on the pop-up confirmation that comes up.

Anyone else with questions like these though, I think already said it all in the second post on this topic :) This option actually can save people a lot of time and sP because if you accidentally train a stat, it saves you the need to wait out the accidental session(s) and then buy leeches to delete the extra stats. Or, a more common case would be accidentally training level before the other stats are done, since a higher level means the training costs more.