"Fighting" is a very 'simple' thing. Simple in the sense that your objective is very clear, immediate, easy to focus on. There's not much ambiguity about what you're doing, and it's easy to tell yourself that you've got no choice - hence, no need (or indeed chance) to think carefully about all the other things you could be doing.

To people who are tormented by self-doubts and what-ifs - i.e. to approximately 93% of all humans - the thought of "going down fighting" can be quite comforting. Particularly if they've been under a lot of stress/doubt recently (as they generally have, by the time they come to make a decision like that). The alternative, in general - assuming you can't win the fight - is to make a conscious choice to give up something of value (often, very great value - such as your home or family). That's a very hard decision to make. Choosing to "go down fighting" absolves you of the need to live with it, even if the end result is much the same.

In the context of gaming: this last consideration still applies surprisingly strongly. The chief difference being that your motivation is modelled differently. An imaginary family means orders of magnitude less to the player than a real one, so games invent things like "alignment" or "disadvantages" to apply similar levels of motivation to a PC.