Declaring that he was opposed to using this unusual animal husbandry technique to clone humans.

这里的was opposed to 后面怎么可以连doing结构呢

此处to是介词
类似的短语还很多
be/get used to
look forward to
be devoted/committed to
be addicted to
object to
turn to
等等，总之要把见到to就当不定式符号的思维丢掉

oppose to doing sth.：反对做某事 这是一个词组搭配 再看看别人怎么说的。