You should take the specified differential impedance of 90 ohm +/- 15% simply as a fact. Asking "why is it so" is a question of technical history. I guess, that the designers of the USB standard found 90 ohm more easily to achieve with a shielded twisted pair.
USB uses both single ended and differential signaling by design. Refer to the USB standard for SE0 (single-ended zero).
The standard requires a receiver to detect a differential signal of 200 mV (7.1.4 Receiver Characteristics), in so far you can't use single ended logic if you want to comply with the standard. But if you don't need to, it works well with reduced requirements. I have e.g. made a full-speed USB analyzer using 3.3V CMOS logic inputs for D+ and D-.