Jesus did say “Everyone will hate you because of me.” (Luke 21:17)
John 15:18-23
New King James Version
The World’s Hatred
18 “If the world hates you, you know that it hated Me before it hated you.
19 If you were of the world, the world would love its own. Yet because you are not of the world, but I chose you out of the world, therefore the world hates you.
20 Remember the word that I said to you, ‘A servant is not greater than his master.’ If they persecuted Me, they will also persecute you. If they kept My word, they will keep yours also.
21 But all these things they will do to you for My name’s sake, because they do not know Him who sent Me.
22 If I had not come and spoken to them, they would have no sin, but now they have no excuse for their sin.
23 He who hates Me hates My Father also.
https://www.biblegateway.com/passage/?search=John+15%3A18-23&version=NKJV