We need to clarify Rand’s use of the word “objectivity.” She did not use it to mean “dispassionate” or “unfeeling” or “universal.” She used the word in a metaphysical and epistemological sense.
Metaphysically, objectivity means A=A, independent of your consciousness. Facts of reality are what they are, independent of anybody’s beliefs or feelings. Wishing won’t make it so.
Epistemologically, objectivity is the recognition of the fact that in order to understand the facts of reality, you need to use reason and the rules of logic, not your preconceptions or feelings or somebody else’s opinion. This is the only valid way we have of understanding reality. These are the only proper tools of cognition. Emotions, on the other hand, are our response to reality, not a path that leads to understanding. Emotions have their place, but they are not tools of cognition. Again, wishing won’t make it so.
So objectivity does not require us to abandon our feelings and values, provided they are a rational response to objective reality. Rational, in this context, means appropriate with the facts. You wouldn’t normally feel love when confronted with a terrorist., or feel terror in a field of daisies . . . unless there were some extraordinary extenuating circumstances. And even then, or *especially *then, you need reason to sort out an appropriate response.
Or let’s say you’re just meeting someone. You wouldn’t start out by valuing that person, except in a very general sense that you’d value any random human being. Rather, you’d observe him and rationally begin to draw inferences. Then you’d, over time, develop an opinion of him . . . and the appropriate feelings. In this context, your feelings are objective, i.e. based on the facts of reality. And obviously we can be mistaken . . . we are not omniscient . . . and if we perceive new or changed facts of reality, our emotions should change accordingly.
But if someone disregards the facts of reality, in favor of their feelings . . . e.g. continuing to love someone, regardless of their dishonesty and obnoxious behavior . . . those feelings are neither rational nor objective. Or if you have a phobia . . . say, a fear of driving over bridges . . . that fear is inconsistent with the facts of reality, and is therefore neither rational nor objective.
Rand (and other Objectivists) wrote extensively about the relation between reason and emotions. I’ve barely scratched the surface here.