"On the personal side of things, I thought any income was taxable."

The partnership is its own entity. It reports through the K-1.

If the partner takes out more than their ownership share (their basis), you would have to figure out how they managed to do this, and that is when things start to get complicated and might be taxable. Example: The partnership takes a loan, and instead of leaving that in the partnership, each partner takes an amount. They either Borrowed from the partnership (and need to repay it) or they are treating that as theirs to keep, which starts to trigger considerations such as Taxable to them, but wasn't income for the partnership.

Taking their own equity out of the business each tax year doesn't make it income for them or expense for the partnership. That's why I pointed out, you are confusing Cash Flow and Income. These are not synonymous.