As a personal rule, for every 1 minute I spend doing something, I make sure to spend 5 minutes thinking about what I'm doing. Does my intended solution solve the problem? Is it missing anything? Does it introduce any new issues? Does it solve the problem, but lead the code down a bad or inflexible road?
Writing and shipping code fast can be tempting, but that speed often impairs insights of what that code actually does, or what implications the code may have down the road. Spending more time thinking than doing might seem less productive, but that is only true in the context of immediate results; in the long run, being considerate and deliberate with your code will have huge payoffs.
The major benefit of TDD is that it forces developers to think about their code before writing any of it, and later reap the fruits of that deliberation. If you do that thinking anyway, without needing TDD, then the process (writing tests first) might not be as practical for you.
As with all things, it comes down to knowing your own limits, and using tools and processes help soften those limits.
If you're trying to "sell" it to your manager, keep that same thing in mind. What problems does the company experience regularly that would be solved or minimized by TDD? If the company gets along fine without it, then TDD might not be necessary. When pitching it, be sure to have actual, relevant facts ready: How many bugs make it to production? How often is a feature requested, but existing code makes it difficult to implement? Do people often find themselves asking "I wish I had thought of that earlier"?