This foe is beyond any of you

From Gandalf's perspective, he's dealing with a fellow Maiar spirit, but one empowered by Morgoth to an unknown degree. It's a frightening prospect since there's no way of knowing if Durin's Bane is a relatively low level minion or a potential trump card hidden away for an unknown purpose. At a minimum, it's laid claim to what may be the greatest city in Middle Earth's history, but was that by virtue of it's power or it's ability to instill fear?

From the Balrog's perspective, Gandalf is a fellow Maiar, one predominantly in service to Manwe. Gandalf carries an Elven runeblade, and one of the 3 rings of power, Narya, which can manipulate fire. It may understand the potency of the sword well enough, but the RoP were likely made after it found it's way under the mountain. It also knows that Gandalf has been running away from a small army of orcs for some time. His unwillingness to hold his ground could be taken as a sign of weakness.