Question: Why did Charity Burbage encourage magical folk to reproduce with Muggles? I know that not all of them hate Muggles, but what did she particularly like about wizards pairing up with them?
Answer: Simple genetics. Wizards staying within the wizarding world are trading the advantage of preserving the wizarding gene for the many disadvantages of breeding within a smaller and smaller genepool.
Answer: Burbage was probably teaching students to go against blood purity as a Muggle is no different to a wizard. Death Eaters are blood purists, so they aren't happy with this.
Answer: She may not have gone out of her way to encourage it at all, but in Voldemort's eyes, anything other than actively condemning the interbreeding of wizards and Muggles would be tantamount to "encouragement."