That is, if the $4K/month is actually $3K child support and $1K alimony, the father's taxable income will be reduced by the $1K, but he's paying taxes on the rest. The ex-wife will pay taxes on the alimony received but not on the child support received.
This is one of the several reasons why women seek child support rather than alimony in divorce proceedings.
Seems like he needed a better divorce attorney.
You mean "child support".
Alimony is a payment directly to the ex-spouse, for the ex-spouse's enjoyment / benefit.
Sometimes in a relationship both parties agree that it is best if one party (usually the mother) puts aside her career in pursuit of raising the children. This party is at a disadvantage after a divorce, and in some cases it may be reasonable to compensate for it.
Ideally this should be a tiered system when payments wind down over time (but usually isn't).