UPDATE 29/3/2015. Dear friends, since writing and making this article and video above, it must be noted this statement by Jesus is most probably referring to believers and NOT (non believers) for the very fact that (non believers) are Not seeking to enter the strait gate, because they simply do not believe it exists.
Gill's Exposition of the Entire Bible Strive to enter in at the strait gate,.... What is meant by the strait gate, and by entering in at it; see Gill on Matthew 7:13. To "strive", is to be diligent in the use of means; to search the Scriptures with care; to attend on the preaching of the word with constancy, neglecting no opportunity; to pray earnestly for spiritual light, knowledge, and grace; to contend with every enemy that opposes the salvation of the soul, as sin, Satan, and the world; to bear all reproaches and persecutions, and press through all difficulties, for the prize of the incorruptible crown:
the metaphor seems to be taken from the striving, wrestling, and combat in the Olympic games, for a corruptible crown: for many I say unto you, will seek to enter in, and shall not be able: either when it is too late, when the door is shut; or else before, very faintly, in a superficial manner, from a mere natural affection, from a principle of self-love, which leads every one to desire happiness; and by very indirect and improper methods, by their own civility, morality, and righteousness; by works of the law, moral, or ceremonial; or by a profession of religion, and an outward compliance with the ordinances of the Gospel, and not by Christ, and faith in him.