If you look at the original Greek word which the English term “follow me” is derived, (ἀκολουθέω akolouthéō; contracted akolouthṓ, fut. akolouthḗsō, from akólou-thos (n.f.),) you will see it means more than the English term conveys-
following Jesus appears as an independent concept apart from any outward act or momentary circumstances of time and place which union with Him might involve. See also Mt 8:10,22,23; 12:15; 14:13; 19:2; 20:29,34; 21:9; 26:58; Mk 2:14,15; 3:7; 6:1; 10:21,28,52; 11:9; 14:13,51,54; 15:41; Lk 5:11,27,28; 7:9; 9:11,49,59; 18:22,28,43; 22:10,39; 23:27; Jn 1:37,38,40,43; 6:2; 13:36,37; 18:15; 20:6; 21:19,20,22; Ac 12:8,9; 13:43; 21:36; Rev 6:8; 14:13; 19:14. With reference to time, akolouthéō means to follow thereupon (Rev 14:8,9, to follow in succession, succeed; 14:13, their good deeds accompany them to the judgment seat of God). Figuratively it refers to spiritual or moral relationships (Mt 10:38; 16:24; Mk 8:34; Lk 9:23; Jn 8:12; 12:26).