Jamieson, Fausset and Brown on Luke 13:24

24. Strive--The word signifies to "contend" as for the mastery, to "struggle," expressive of the difficulty of being saved, as if one would have to force his way in.

strait gate--another figure of the same. (See on Mt 7:13, 14).

for many ... will seek--"desire," that is, with a mere wish or slothful endeavor.

and shall not be able--because it must be made a life-and-death struggle.