When people say “you know you are important to me” the best answer is “I don’t know.” Think about it before you answer. There’s great social pressure to say “yes, of course I know that” when asked by a parent, spouse, boss or old friend, but that pressure confuses your abstract feelings about a person with an evaluation of how they behave towards you. Feelings and actions are different things, and the fact someone feels you are important to them doesn’t guarantee they treat you well, or that they should be important to you.
As important as feelings are, if they don’t influence behavior feelings have little meaning for anyone but the person having them. If I love you, but treat you horribly, or ignore you, or behave selfishly and never consider your needs in any of my actions, I’m betraying those feelings (whether I realize it or not). It’s therefore not about whether I love you or care about you, but how my behavior towards you reflects those feelings. That’s the basis for healthy relationships: a connection between feelings and behavior, or emotions and actions. All too often our actions and emotions are disconnected from each other. Either through fear, disfunction, or ignorance, our emotions never make it out of our hearts and into actions that have meaning for the people we care about most. Integrity is the proximity of your beliefs to your actions, and we need more integrity in this world.
There are similar truths in the workplace. To be told a project is important, but not to get the resources you need to do it well is a kind of lie. It’s a disconnect between the word “important” and any action that would embody importance. The person with the disconnect might not realize they are betraying themselves, but they are. Either you’re not important enough to deserve the resources and they’re deceiving you by using that word, or they are incompetent in not giving you the resources your importance merits.
It’s a low bar to ask “you know you’re important to me, right?” The better question is “does my behavior express to you how important you are?”