What does the ‘I’ stand for in DEI?

Say a man thinks nursing is for women and not for men. Say an employer wants more nurses irrespective of sex. Is that employer engaging in DEI if they spend more money on male re-education than on recruiting women?

Depends on why they're spending it that way, not whether they're spending it that way.

The problem is the "male re-education" and "recruiting women."

They should just have a recruiting budget and a re-education budget. There should be a way to determine the best spend of the money. Maybe one method of generating a nurse is cheaper, or produces a better quality employee. When you try to have the process generate "at least this percentage of [male/brown/etc] people" instead of just generate the most/best candidates, then you have DEI. The process doesn't produce the most, or best quality employees --it works to force an outcome that is unrelated to employee skill or best business practices.