1 Timothy 2:12 is inspired by God.
That doesn't mean that it is a command that is applicable to us today. Where does it say that it is? How do you know that it wasn't inspired by God as a solution to a particular problem that Paul was facing at the time? What gives us the right to assume that it applies to us too and is definitive teaching on the subject?
Were Paul's words in 1 Timothy 5:11-15 about not giving financial help to widows under 60, inspired?
Was he inspired when he called such widows gossips and busybodies? If so, then presumably his words apply to us today - if we follow your logic of applying ALL verses of Scripture to everybody. So any women in your church/community who have lost husbands in war, and been left as single parents, you can tell them that Scripture says they are gossiping busybodies and deserve no financial support from the church.
Was Paul inspired when he taught about treating our slaves well? If so, then presumably Wilberforce sinned when he abolished slavery and we should all have slaves, as they did in Bible times, so that we can follow Biblical teaching about how to treat them?
Was Moses inspired when he gave the law to the Israelites? We know that Jesus said that he had come to fulfil the law, but that law is still in the OT - the compilers of the Bible did not say "it's irrelevant, leave it out." Following your words that "it's either all inspired or not at all", should we be keeping the Jewish law that was never given to us anyway?