Why would you ever attempt to outrun a ship before or during a fight? (should you always take a blue option)

Blue options to escape, like any other offer to escape, are generally not the best choice. They earn their right to exist by being better than the other escape option, which, in the case of those events, doesn't always succeed, and may have other penalties.

If you're confident you can handle the enemy, then take the fight (you can usually tell what you're going to fight by the event text).

Blue signifies conditional option, available to you because you've fulfilled some prerequisites. It's not "the best" option. Even in tutorial it's said that blue is often the best option. Often, but not always.

Occasionally, there are horrible circumstances, like you only have enough power for weapons or shields, and you're in a nebula that has halved your power (guaranteeing either a loss or horrible horrible damage). Then, you might run.

Or, you're low health and one stop away from a known store to repair.

Usually you want to fight and get a reward, but it's hard to say "always" in FTL.