first, frogs dont drink through their mouths, they drink through their skin. that being said, human hands are DIRTY and you wouldnt want someone shoving their fingers in your mouth hehe. Also, i think a human is a little more hardy when it comes to germs than frogs. So if you absolutely need to pick your frog up, please wear gloves or at least wash your hands before and after.

second, red eyed tree frogs are not to be played with. they are honestly not supposed to be held or disturbed. If you wanted something to play with, you shoulda got a dog lol. They are pretty much boring globs of green on the side of glass most of the day then wake up at night to eat, soak, call, etc. that is the most enjoyment you will get out of your frog.

Frogs are easily stressed out. I am a firm believer that stress can kill a red eye. also stress can do a lot more things. Say your frog were to have parasites, stressing it out can cause an outbreak of those even after you get the frog back healthy.