It is mentioned in The Hunger Games: Mockingjay that Katniss wanted to run away from District 12, she suggested this to Gale while next to the lake that Katniss's father used to go teach Katniss how to swim.
Why did Gale not comply with Katniss and take the opportunity to run off to avoid the Games?
It is a lot clearer in the book.
They where both quite willing to run, but Gale expected only Katniss, himself and their families. He did start turning his opinion around when Katniss mentioned she's taking Haymitch and, of all people, Peeta, too!
In the book, Katniss then mentioned an uprising happening in District 8, which caused Gale to see an opportunity to bring down the Capitol, without any need to have Peeta along for a desperate escape that may easily fail.
Also, it was winter, so finding food on the way would have been quite a challenge, too. Actually, the whole thing may have played out differently if only it had been spring.
In the book, it is because of all the people he feels responsible for and would need to bring -- her mom and sister, his parents and siblings, etc. They would not be able to travel and hide very easily with so many people. She comes off as very selfish in the scene, while he is the practical one.
