I agree with you on how I define love as well. I define it as a series of actions or choices that one makes in thier life towards someone. I came to this from an abusive relationship where we said we "loved" each other - based on how we felt, but in reality there was very little love in there. I think it was more codependency than anything.
However- I can see that with even your description of love how someone could still feel insecure or unsure of your position in thier life based on how you interact with others. You say you will always love someone, but you also say that how you show that will change.
This is a bit confusing, because if you don't show love via actions, etc. in the way that someone would interpret as "loving". Then to them, it doesn't matter if you "love" them or not - because what really matters to someone is the actions, not the theoretical thought from afar.
For example, if someone was a murderer or an abuser (ok an extreme example to prove a point) you might always love them, but you might not decide to even be around them, talk to them, etc. Or as a nother example, you might always love someone - but time spent on another relationship detracts from what you used to do as "acts of love" to the first relationship.
To you - this is all great... but to the other it can be a source of internal debate, threat, and fear.... all adding to insecurities and jealousy. Simply because in the end - noone really views love as just a feeling... it is how they are treated by someone that really shows love.
just another ramble.