Thomas Wyatt is kind of a big deal: he's often credited with introducing the sonnet into English (a 14-line poem). Why? Well, he translated the Italian poet Petrarch's famous sonnets into English. It turns out Petrarch wrote a lot about unrequited love, and so it seems like Wyatt had this on the brain.
Many of Wyatt's poems are about this very topic, and "They Flee from Me" is no exception: it's all about the speaker's abandonment by women. If you take a quick look at a list of Wyatt's poems, you'll notice that many of them are about love and the pains that being in love can often cause. With titles like "My Heart I Gave Thee, Not To Do It Again," "Farewell, Love, and All Thy Laws Forever," and "How Oft Have I, My Dear and Cruel Foe," it sure seems like Wyatt thought a lot about love. He's like a precursor to the old school country singer, crooning about cheating hearts, crazy love, and the mystery that is women.