According to Pliny the Elder, the standards of the legions originally featured a modest menagerie of creatures, including wolves:
"Marius, in his second consulship, assigned the eagle exclusively to the Roman legions. Before that period it had only held the first rank, there being four others as well, the wolf, the Minotaur, the horse, and the wild boar, each of which preceded a single division." (10.5)
By the time Marius confirmed the eagle's primacy, however, it was already recognized as the most important military emblem. The basic reason - though not stated explicitly by Pliny (or, as far as I know, by any other ancient author) - seems to have been the eagle's close associations with Jupiter and victory. Pliny, in fact, claims that real eagles were naturally drawn to the legions, and tended to nest wherever they camped - the bird of victory seeking out an ever-victorious army.
Wolves were, of course, fundamental to the Roman foundation myth, and were closely associated with the war god Mars. But they were also troublesome pests, and their appearance was often regarded as an evil omen (e.g. Livy 3.29). The wolf, in short, had less salubrious and glamorous associations than the eagle did - and this seems to have made it less congenial as a symbol. It should be noted, however, that wolves were not entirely banished from the legions: for centuries, Legio II Italica used one as its emblem.
You might be interested in this thread "Did the Roman Empire have a flag?," with responses by /u/toldinstone among others. For your question specifically, it seems that the eagle was primarily associated with soldiers.