Feelings are not tools of cognition, so you never do something just because you "feel like it". But what if someone has feelings, that he thinks are irrational? Is that man not sufficintly rational enough, at least in his subconcious? Or do such things happen to everyone?
When we say a person is "honest" or "courageous" or "rational", it's because we consider their actions to be, in general, virtuous. But being such a person doesn't mean that one is never tempted to do something which is wrong, or that one never has an "irrational" emotion.
When a man is being rational, he bases his actions on reason, instead of on emotion. The emotions he has at the time do not figure into whether he is rational or moral.
Emotions are products of one's psychology. Emotions are generally caused by conclusions formed, as a child, in one's childhood environment. Such conclusions, even if innocently made, can be mistaken since one's childhood environment isn't necessarily representative of the world as experienced by an adult.
The emotions we have as adults automatically happen in the present. There is no moral status to be attributed to one's emotions. Rationality and morality pertain not to one's emotions, but to one's thinking, and one's actions, respectively.
One cannot say with certainty that everybody has irrational emotions. Presumably someone might exist with a perfectly healthy psychology (like an Ayn Rand hero). But what is true is that the presence of irrational emotions does not preclude anyone from being rational, and moral.
Improving one's psychology is very difficult, and usually very time-consuming. Having an unhealthy psychology is a clinical, not a moral issue.
Yes, it is sometimes possible to fault someone for his psychology, since man is a being of self-made soul, but doing such is easy to get wrong, and it's usually counter-productive. After all, a man with an unhealthy psychology bears a burden, and it would be wrong to blame him for his burden, especially if he carries it well as an adult.
What matters, morally, in the present-day is not psychology, but thinking and action. Psychology is "water under the bridge" morally speaking, and it sets the emotional context within which one must make make one's present-day decisions, moral or not.
A man who struggles to act well, and succeeds despite an unhealthy psychology, is heroic, not depraved.
For more about this topic, please see Ayn Rand's essay: "The psychology of psychologizing".