I believe Christ is speaking of total devotion.
In the parable preceding your passage, the feast is prepared, but then:
Luk 14:18-20 And they all with one [consent] began to make excuse. The first said unto him, I have bought a piece of ground, and I must needs go and see it: I pray thee have me excused. And another said, I have bought five yoke of oxen, and I go to prove them: I pray thee have me excused. And another said, I have married a wife, and therefore I cannot come.
Then He says:
Luk 14:26-27 If any [man] come to me, and hate not his father, and mother, and wife, and children, and brethren, and sisters, yea, and his own life also, he cannot be my disciple. And whosoever doth not bear his cross, and come after me, cannot be my disciple.
The true disciples are these:
Luk 14:33 So likewise, whosoever he be of you that forsaketh not all that he hath, he cannot be my disciple.
The Lord doesn't acknowledge halfway followers and fence-sitters. You are either devoted to Him, or not, love/hate, hot/cold.
Like this:
Luk 16:13 No servant can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
And this:
Rev 3:15-16 I know thy works, that thou art neither cold nor hot: I would thou wert cold or hot. So then because thou art lukewarm, and neither cold nor hot, I will spue thee out of my mouth.
Sonia