or
A) Because his bosses at White Star lines were leaning on him to break the Atlantic crossing speed record, which had recently been set by a competitor.
B) He had been quietly informed that there was fire in the coal bin.
Reason B might have been kinda understandable if true. Reason A wouldn't have been a good reason but it would have been a "reason-reason" nonetheless.
Stockton Rush was a psychotic narcissist. Personal pride and ambition are really suck-ass reasons to lead other people to suicide, especially for a Princeton man.
One has read that the young Pakistani man really really really didn't want to go on the Titanic cruise, but dad was obsessed with the matter and was insistent. When dad says you go, one goes, if one is a good son...
It would have been his last trip, he should have done what a good Captain would do and be prudent. The graveyards of full of people who wee not prudent when they should have been, but the Captain needs to protect his passengers.