you can be possessive and still love, and you can have narcissism and still love.
We are humans, not programmed robots.
Narcissists are void of empathy - so they can't genuinely love. Also - there is no love without freedom, so I am not sure what you mean by "possessive", but that can't include controlling another person's will.
I think this article does a great job of breaking down what "love" entails (this is written in the context of marriage - but it can be expanded to many relationships in general):
Quoting from Covenant Keepers------>
The attributes of love
1. Giving love. One of the most important characteristics of true love is that it gives. Jesus explained to Nicodemus that
“God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life” (John 3:16). God loved us so much that He gave us His most precious gift, His Son. God continues to love us by pouring His blessings upon us day after day. Giving is the foundation of true love. Consider, are you the giver in your relationship or are you the one expecting to receive?
2. Sacrificial love. Love by definition must be sacrificial to be true love. In the Old Testament when God asked for an unblemished animal to be offered to Him on the altar, it was to be the best sheep or goat (Num. 18:29-30). The people were not allowed to give an animal that was sick or diseased (Lev. 22:20-24; Mal. 1:8). To give their best animal would have been a true financial sacrifice for them. This is exactly how God gave His love to you.
3. Serving love. True sacrificial giving will also inspire loving service to your spouse. Paul encouraged all believers that we should by
“love serve one another” (Gal. 5:13). Therefore, if you love your spouse, how are you serving him or her in practical ways?
4. Love freely given. One of the most misunderstood aspects of marital love is the fact that true love is totally voluntary, unforced, and free of manipulation or control. God declared that this was the way He loved His people when He promised,
“I will heal their backsliding, I will love them freely” (Hos. 14:4). The word
freely in this verse means voluntarily. In other words, God is explaining that His love can’t be forced or manipulated by others and that He has chosen to love His people for His own reasons. Jesus said the same thing about the love that motivated Him to go to the cross.
“Therefore My Father loves Me, because I lay down My life that I may take it again. No one takes it from Me, but I lay it down of Myself” (John 10:17-18). Jesus was declaring that no one was controlling His decisions. He was voluntarily giving up His life because He loved us.
5. Submissive love. It is important to note that before Paul commanded a wife to submit to her husband or a husband to love his wife, he commands both to submit to each other. All should be
“submitting to one another in the fear of God” (Eph. 5:21). Why? Because mutual submission is a necessity for all relationships including marriage. Likewise, Peter commanded,
“All of you be submissive to one another, and be clothed with humility, for ‘God resists the proud, but gives grace to the humble’ ” (1 Peter 5:5).
6. Supporting love. Why is it that many marriages seem to degenerate into a competition between two people who should be supporting each other? It is simply because one or both partners do not sense that the other truly loves them. They don’t perceive that their spouse has their best interests at heart. This is not the Scripture’s definition of a loving relationship. The apostle Paul instructs:
“I have shown you in every way, by laboring like this, that you must support the weak. And remember the words of the Lord Jesus, that He said, 'It is more blessed to give than to receive’” (Acts 20:35).
7. Kind Love. Quite often when couples come into my office for marriage counseling they will sit in front of me and begin to speak to each other in the most rude, harsh, and critical manner. I will immediately stop them and ask if they truly want to reconcile and renew their love for each other. They almost always declare, “Oh yes, we desperately want to reconcile.” I then explain that their unkindness to each other is completely contradictory to this stated desire.
8. Understanding love. Another complaint I regularly hear from couples is the lack of understanding in their marriage.
9. Laboring love. To demonstrate true love you need to take practical actions that constantly reveal your love.
10. Gentle love. When you consider the topic of love do you connect love with gentleness? Many do not understand this attribute of love. However, Paul associated these two qualities together many times. He asked the Corinthians if they wanted him to come to them with
“a rod, or in love and a spirit of gentleness” (1 Cor. 4:21). Paul also encouraged the Ephesian church to walk in
“all lowliness and gentleness, with longsuffering, bearing with one another in love” (Eph. 4:2). In other words, love is seen in a humble, gentle, and longsuffering attitude. ~
What It Means To Love Your Spouse