Same reason why Gmail uses their own emojis rather than the system ones — (as said above) branding. When you send a tweet, Twitter wants it to look identical across all devices. The classic native UI vs cross-platform UI debate in a nutshell.
Cool, so instead of actually serving text, they could also just serve up little SVGs for each letter. Because god forbid the recipient chooses a different font than Gmail!
Twitter is a media between people. Removing emoji representation differences on user devices is a way to hopefully reduce misunderstandings between users.
