If you want to learn on bikes bit by bit, repairing or upgrading old ones is a good start.

Two things work against you building an all new bike from scratch:
1. Bike manufacturers get such a huge discount on parts that if you buy the very same parts yourself, you pay more than the new bike. Even if you buy a new bike and replace 1 or 2 components you still are better off financially.
2. Bikes are very simple, no big challenge in principal. The challenge is that there are dozen of different sizes and standards for the very same thing and you need the special tool. And when you look at manufacturer's websites, you don't get a lot of information (like what exact tool to use, what exact size etc.). If you already have an old bike and replace parts, you can measure yourself and find out what is needed. If you buy a frame to begin with, you don't get all that information before you have the frame (they don't even give you weight of the frame in many cases). You need to be quite experienced and even then you may mis-buy some things.

If you don't mind #1 and #2 and just want the experience, go for it and research the crap out of it. but if you want to save money and want a rideable bike now, better buy a new or good used one.