Does that mean you shouldn't bother trying learning as much as possible? Of course not. If you want to truly master animation, you should absorb as much information as you can about the styles of animation, its history, the end-to-end process for the area of animation you're focused on, and even as much as you can about areas where you're not. But the first thing you should focus on is the basics, and the second is on honing your specialty. As you build your career as an animator, you'll find yourself occupying many roles on your way up the hierarchy of a typical animation team, or even as you work your way up the various quality and skill levels expected of an independent freelance animator. These roles will teach you about diverse things, but still won't teach you everything.
Very few people can be a one-man (or one-woman) animation team, though computer animation software has made it easier to trim out the people required to produce quality animation. Still, most people who try to be a jack of all trades end up, as the saying goes, master of none. You're more valuable to an animation studio as someone who's excellent at keyframing or someone with an exceptional talent for texture mapping than you are as someone who's just okay at everything. While there are a few virtuosos who manage to be geniuses at everything, you should identify your strength and focus on becoming the best at that.
This could mean being the best storyboard artist ever, or the best background artist, or the best at rigging bone systems, or at modeling realistic 3D faces. If the artistic side of animation isn't your forte, you could be a scriptwriter, a sound specialist, a timing specialist, or numerous other key roles that are just as essential to the process as the actual animation. It can also mean focusing on a specific industry, whether you stick to traditional 2D television animation or get into something specific like medical animation or architectural animation. You could even be a voice actor.
The point is to find a balance. Remain aware of the industry; understand the ins and outs of the process; absorb what you can through experience and learn the skills you need in each role you take on. Put yourself 100% into everything you do, but don't try to put yourself 100% into everything. You should know where you fit into the grand scheme of things, and how your efforts contribute to the whole, but until you've had time to work your way through the industry and build your skillset over the course of your career, you won't be able to learn everything all at once.
