This is actually quite an interesting question because it depends. Some trainers prefer to wait until their growlithe learn Flamethrower, as it’s sometimes easier (by which I mean cheaper) to let it learn that move naturally, rather than use the TM system. Others prefer waiting until their growlithe learns Crunch, which typically happens much, much later. On the other hand (compared to both options), some trainers prefer evolving their growlithe right away, as arcanine is very adaptable to the TM system, and only younger arcanine can learn Extreme Speed (a move inaccessible to growlithe). Likewise, such trainers very rarely have use for Crunch, or if they do, they also are acquainted with a move relearner or tutor capable of teaching newly evolved arcanine Extreme Speed far later than they would naturally.
In short, the answer is it depends in part on which move you would like your arcanine to know. If you’d prefer a faster arcanine, evolve it sooner, but a stronger arcanine (or an arcanine that requires fewer TMs) should be evolved later. (There are no differences in health if you choose to wait. In fact, the vitality an arcanine gets through evolution means that a growlithe that waits to evolve is just as healthy as one that’s evolved immediately.)
Ultimately, though, waiting until the time is right is also sound advice and perhaps the better avenue, especially if your growlithe has a strong opinion one way or another. If your growlithe is impatient to evolve, consider doing so sooner, whereas a hesitant growlithe should hold off until they’re ready.
Best of luck!
The Pokédex According to Bill 