καὶ τότε σκανδαλισθήσονται πολλοὶ καὶ ἀλλήλους παραδώσουσιν καὶ μισήσουσιν ἀλλήλους·The Greek term σκανδαλισθήσονται means not only to be offended, but is the source of our English term to be scandalizedm and is actually stronger than merely taking offense. This taking offense, whether or not offense was intended, will serve as an excuse for people to betray and hate each other. Offense, hatred and betrayal often go together.
And then many will be offended and they shall betray each other and shall hate each other. (Matthew 24:10)
In Jesus's prophesy, these events follow the betray and murder of the disciples. The implication is that first they betray the disciples because they hate them (because they hate the Lord of the disciples) but the hatred and betrayal does not stop there. Having betrayed the disciples, they then proceed to betray each other proceeding in a vicious cycle. This cycle can be seen throughout human history. It is a sure sign of ill times.