1) That was written by Paul and not Timothy.
2) If you only look at what supports your position instead of both sides, you will find yourself at odds with reality.
Simple logic:
Ignatius were familiar with the letters and accepted 1 and 2 Timothy as genuine letters from the apostle Paul. Ignatius, the Bishop of Antioch (67-110 A.D.), was the pupil and friend of the Apostle John. Already, you are 40 years off on the back end because Ignatius already knew about the letters before he died in 110AD
Clemente of Rome made allusions to it in 95AD which make your front end wrong too.
Further detailed studies will place it more between 62-66 AD