I am saying that 2 Timothy 3 cannot be properly understood until we read 2 Timothy 1 and 2 Timothy 2. Which is the case with any book, by the way: you read it from the beginning.
The consecration of Timothy is here:
6 For which cause I admonish thee, that thou stir up the grace of God which is in thee, by the imposition of my hands.(2 Timothy 1)
The instruction to pass on the teaching authority to others is here:
2 And the things which thou hast heard of me by many witnesses, the same commend to faithful men, who shall be fit to teach others also.(2 Timothy 2)
The specific instruction to ordain certain men is in the previous letter:
1 A faithful saying: if a man desire the office of a bishop, he desireth a good work. 2 It behoveth therefore a bishop to be blameless, the husband of one wife, sober, prudent, of good behaviour, chaste, given to hospitality, a teacher, [...]8 Deacons in like manner chaste, not double tongued, not given to much wine, not greedy of filthy lucre: 9 Holding the mystery of faith in a pure conscience. 10 And let these also first be proved: and so let them minister, having no crime.
(1 Timothy 2)
19 Against a priest receive not an accusation, but under two or three witnesses.
[...]
22 Impose not hands lightly upon any man
(1 Timothy 5)
The fact that not every time a figure of authority is described in the scripture, his consecration is also mentioned, shows nothing. The fact that not every laying of hands describes the sacrament of Holy Orders does not deprecate the context shown above, where it is.