This time is the last time in comparison with the first time, which is the time of the Old Testament, the preparatory time. The last time is final. It is the last period in the ordering of salvation, after which there will be no other such period (cf. 1 Pet 4:7 and note).
Insolent mockers, or scoffers, are people who will not merely deny or reject the teaching about the second coming of Christ and the events joined with it. They will insolently mock this teaching, turn it into ridicule, and lead others also to deride it.
This does not mean only wolves in sheep's clothing, but real wolves in their own form.
According to their own lusts means that they act against the law of Christ and are led by their own impulses and strivings, which are fleshly and sinful. Here is the root of their error, or false teaching: fleshly lusts (1 Jn 2:16).
What sort of people are these? They are a different class of Christ's enemies from the false prophets or false teachers mentioned in the second chapter. They have this in common with those teachers: they sink into filthy fleshly lusts. Yet these are also mockers and scoffers, which is not seen in the former.
The appearance of these mockers and scoffers is indicated in Acts (Acts 20:29) and by the apostle Paul (1 Tim 4:1; 2 Tim 3:2-5ff.). They appeared soon after the apostles. They always have existed and, according to the word of Christ and the apostles, will exist, to their own perdition and to the perdition of those deceived by them.
And saying, and so forth. They say this not only in their corrupted heart or thought, but openly and mockingly. Their very aim is to trouble others, especially the good and pious.