Well familiarity does breed contempt. Back when they were in the Homeworlds, as folks said, grudges were born and carried on over the years and because both sides are darn proud with any refusal to back down, it was an ugly wound that festered between them.
Now days they are more like friendly rivals, but the Horses are also basically smart enough to not poke the Bears, considering the Bears tend to massively over react to poking.
The Bears enemy focus switched to the Nova Cats after they emigrated to the Inner Sphere. Mainly because the Cats held the idiot ball and kept poking and deliberately irritating their much larger and more powerful neighbour who then finally had enough and crossed the border. At which point the Cats acted like the injured party.
It got so bad that the next time it happened, it was a totally undeclared Trial of Annihilation. If the Combine and Republic hadn't stepped in the Bears would have wiped the Cats out.
And Bears are not sues, they are dirty campers :p And I say this as a Ghost bear lover myself. Basically they are the faction who turtles up and just builds and builds and builds and builds whilst everyone else sends out their troops and spends resources on fights etc. And then when someone pokes the Bears, they suddenly find they've poked the largest Tourman the Clans have left. Which is then happily married to a temper that could be absolutely hair trigger at times.
Plus, the Bears have in essence been conquered, by the Rasalhague Republic. They are not a Clan really any more, but an amalgam, and hold enough space and have a large enough military to be called a House by any reckoning. But the other Clans need them, so keep calling them Clan and invite them to meetings etc to hang out and the like. All the while the Bears are happy to sit in their den and build up and build up and....
To quote Ambassador Mollari "If you do not bother them, they will not bother you."