The first thing to note is that Tether is not literally 1 USD, even though it is backed in part by dollar-reserves. It is a derivative of the US dollar, that can fluctuate very slightly in value based on supply-demand principles, and counterparty risk.
A supply-demand event that affects the price of Tether could be one of the following examples:
Bitcoin is doing extremely well and becomes a popular buy. Investors are now getting rid of their Tether to exchange for BTC, causing an abundance of Tether available for purchase. This will make the price of Tether drop.
Volatile crypto assets are tanking sharply, and investors become extremely fearful. They either want to exit the crypto market, or move their money to less volatile assets (such as stablecoins). In either case, Tether becomes more in-demand - causing the price of Tether to rise as there is a shortage of Tethers for purchase.
Counterparty risk refers to the chance that the Tether system could collapse as a whole (remember, it is not fully-backed by dollar reserves). Public perception is affected by news about the Tether ecosystem, which could drive the value up or down.