The Biblical meaning of "hate"
In the Biblical era, the word "hate" (μισεω, miseo) has connotations seldom used today, see Abarim Publications's online Biblical Greek Dictionary entry on μισεω where there are more verses that use "hate" in those senses.
Consulting the standard lexicon Kittel & Friedrich's Theological Dictionary of the New Testament Volume 4 (Λ to Ν, 1967), the word μισεω has an entry with section 5 titled "Hatred and Hating in the New Testament" where the entry's author analyzes the various nuances of μισεω in the whole NT (see concordance). The author wrote 8 sub-sections, dedicating the sense used in Luke 14:26 (along with parallel passages Matt 10:37 and Jn 12:25) as follows:
c. Hatred in Discipleship of Jesus. The requirement for discipleship in Lk. 14:26 (Mt. 10:37); Jn. 12:25 is striking: “Hatred of all we are under obligation to love, including our own souls, is the condition of fellowship with Jesus, of working together with Him.” 26 The reference is not to hate in the psychological sense, but to disowning, renunciation, rejection (καὶ τὴν ψυχὴν ἑσυτου̂), as in the Wisdom literature of the OT.27 Those who become disciples of Jesus must be committed exclusively to Him; they cannot be bound to anyone or anything else. The term “hate” demands the separation of the disciple, and the warning not to love anyone or anything more is the test. This abnegation is to be taken, not psychologically or fanatically, but pneumatically and christocentrically.
Thus, passage context is paramount to interpret a Bible verse. For Luke 14:26, the containing passage Luke 14:25-35 is frequently titled The Cost of Following Jesus. From the context it is clear that what needs to be "hated" is only the part of our family and our own life that forces us to separate from Jesus and the way of life that Jesus wants us to live (such as when our family members object to us converting to be Christian). In other words, when we are in a situation where we are forced to choose, choosing Jesus can be phrased as "hating" our family members, or "hating" the power of sin within ourselves (see Paul's struggle in Romans 7:14-25).
"Love" vs. "Hating"
"Loving ourselves" in Matt 22:39 includes "hating" the sinful parts of ourselves. In that way we give our soul and body a better environment to grow to be more like Jesus (a work of the Holy Spirit). My wife says it's like weeding. When weeding, we need to make sure to "hate" the weed to the core by also taking out the roots of the weed. I think that's what all Christians (not just the Catholic church) understand the meaning of "hate" in Luke 14:26.
"Love" vs. "Using"
You brought up a very good antithesis between "love" and "use" that Pope John Paul II elaborated in his book Love and Responsibility between "loving" someone for his/her own sake for their mere existence made in the image of God even though they can become a burden to you (which he called the "personalistic norm") versus "using", which he labelled as "utilitarianism" EVEN WHEN the other party doesn't mind. See the full treatment in Chapter 1, Part One ("Analysis of the Verb "to use") pages 3 to 28 of this edition where he discusses:
- The person as the subject and object of action
- The first meaning of the verb "to use"
- Love as the opposite of "using"
- The second meaning of the verb "to use"
- Critique of utilitarianism
- The commandment to love and the personalistic norm
Conclusion
The "love" and "using" antithesis should not be confused with the Biblical sense of "love" and "hate". But both senses ARE PART OF the multifaceted understanding of the Great Commandment that Jesus reminded his audience in Matt 22:39.