Actually, it was designated by the government as a habitat for a land tortoise. They made off with 850 of his cattle and told him to get off, he protested. This is their own doing. And while the BLM was formed in 1946, for 47 years they made no issue with Bundy or his parents over the land in which he used to graze his cattle.
But it is funny how the government never made an issue of it in all that time.
You've got a few things confused, but you're on the right track.
1. The government didn't "make off" with any of his cattle. They changed how many they would allow him a permit for. No cattle of his have ever been removed, until last weekend.
2. For those 47 years, Bundy and his family paid their grazing fees - which is why the BLM left him alone. When the BLM changed the rules, he got mad, and decided to both stop paying his grazing fees, and ignore the limits to the number of cattle he could graze.
You don't get to ignore laws that you don't like - or rather, you can but you've got to face the consequences when they come due.