A UBI is a method of achieving the same effect as progressive taxation without the complexity and perverse incentives of tracking everyone's income and applying different marginal rates.

Suppose you have a tax system with progressive tax brackets and then a needs-based welfare system with benefits phase outs. It turns out, those two things (progressive rate structure and benefits phase outs) basically cancel each other out -- lower income people are supposed to pay lower marginal tax rates but if you're paying a 10% marginal tax rate and then have a 25% benefits phase out rate, that's the same as paying a 35% marginal tax rate. Worse, the benefits phase outs for different benefits often overlap, with the result that lower income people are often paying higher marginal tax rates than wealthy people, and there are some cases when their marginal rates even exceed 100% of marginal income.

So you have two unnecessarily complicated systems that mostly exist to cancel each other out, and to the extent that they don't they're doing something you don't actually want (excessively high marginal rates on poor people). It's better to just get rid of both -- no phase outs is the "universal" part of the UBI, and then you combine that with a uniform marginal tax rate for everyone.

You're basically getting rid of the progressive rate structure so you can lower the marginal tax rates on poor people to the ones being paid by rich people, and if that seems counterintuitive it's because the status quo is very stupid.

It turns out that a theoretically optimal non-linear taxation schedule features a UBI plus varying marginal tax rates (i.e. continuous tax brackets) that start out quite high (but sub-100%) in the UBI-clawback range (to manage the UBI break-even point while still offering a high subsidy to the very lowest earners) become very low for low-to-middle income earners and rise gradually for middle- and high-income earners. That's quite redistributive in intent, but the tax brackets themselves are neither "progressive" nor "regressive". Nevertheless, middle- and high-income earners do face moderately progressive rates.