Well, guess
Also, the national animal of Russia is the Russian Bear. But this "tradition" of having a national animal is a recent thing.
List of national animals - Wikipedia, the free encyclopedia
But there is also an historical reason.
Ever since the time of the Romanovs, Russia has been symbolized by a bear, especially in the west. I don't think we can put date on exactly when this started happening and when this symbolism took root but you know, around the 1700s or later.
Now the Russians never invited this symbolism to their country. I mean there is nothing in the Russian symbolism that hints towards a bear. The Tsarist Empire, like all western nations, had The Eagle as its symbol for the same reason the West has a lot of Eagle symbols -> because of the Romans. I mean the Tsarist flag has a Eagle. The Russian military had and has eagles. Everything is with eagles in all western countries .The USA has a lot of eagles, ofc, its' even the national animal... just like France and Germany and Italy and other countries have some Eagle as the national animal. Romania also had the eagle as national icon on our flag for a long time, now, post communism and post monarchy, it's no longer there.
But the newspapers in the western world, and hence, since Russia started westernizing in the 1700s, in Russia too, had, sometimes as light humor, sometimes as a sign of appreciation and sometimes as an insult, associated Russia with a bear. Slow to start but once it was on the move it was impossible to stop. Or if you wish to use it as an insult, a wild and clumsy animal.