In Star Trek Discovery episode 4, one of the crew members deliberately lets out the (seemingly) murderous and invincible tardigrade. Unsurprisingly, this doesn't end well. Why would she do that when she must have known that a phaser would not stop it and that it would kill her and most likely her crew mate too?
If you're talking about the crew member who, uh, meets an unfortunate end, she says precisely what her motivation is: she wants to please her captain and get the creature's claws so they can develop them into weapons. Yes, she's operating on incomplete/incorrect information, and Burnham tries to tell her so, but she's not in a mood to listen, especially not to The Mutineer.
As far as why let the creature out, rather than letting the crew member in, (1) I'm not sure that would've been any safer, and (2) it's possible that the resources available in the enclosure, starting with lighting, were not sufficient, or were not perceived to be sufficient, to the intended purpose of the operation.