Then who provides that training? And why aren't they knocking on the doors of all the schools in the country?

The big difference from the perspective of the schools is that proprietary software is backed by a big corporation that has made taking care of your needs their business model. There's nothing inherently stopping companies from offering the same quality of service with free software, but in practice free software often means doing things yourself and relying on a community of volunteers.

Meanwhile, for the big corps it's fine if this is a loss leader, because it teaches a new generation to use their products. You've got to get them while they're young, after all.