What is the deliberate fallacy Marvell included in this poetic syllogism?

Critics have been divided as to whether the supposed fallacies in Andrew Marvell's logic were actually deliberate, or simply a failure on his part. A syllogism is a type of reasoning in which two conditions are presented, or two premises laid out, and then a conclusion is drawn from the fact that these two premises share one element. So, IF this, AND this, THEN that. An example of a syllogism which may be fallacious might be:
God is love; love is blind; therefore God is blind.
In this poem, the premises are:
1. If we had "world enough and time," it would be fine for you, my mistress, to be "coy" and for us to spend a long time simply courting each other.
2. But "at my back I always hear / Time's winged chariot hurrying near." We don't have a lot of time, and soon you will be eaten by worms anyway and our window of opportunity will have passed. If you don't lose your virginity to me, you will get old and die a virgin.
3. Therefore, because time is short, we should "tear our pleasures with rough strife / Through the iron gates of life" and just have sex now.
We could pick out at least two flaws in this logical reasoning. First of all, the speaker assumes there are only two possible outcomes for his mistress: either she surrenders her chastity to him now, or she will die a virgin. This is flawed logic: she could just as easily be unwilling to lose her virginity to the speaker because she's actually waiting for someone else. The speaker's logic doesn't admit the third possibility that the mistress might give her youth and beauty to another suitor. Secondly, the speaker takes the mistress's "willing soul" for granted. He assumes that she is simply being "coy" and ultimately does intend to surrender to the speaker, but is insisting upon a prolonged courtship. He does not consider the idea that she is actually uninterested in him.