"Should" men be able to express their emotions within a relationship?
Yes.
Are they?
Typically, no. Two thoughts, by way of explanation...
Firstly, "emotions" is usually a euphemistic code for fear, sadness, and hurt. Few people have an issue with men expressing appropriate elation, surprise, irritation, or controlled anger. It's misleading and confusing to use a general term to mean a small range of the spectrum.
Men feel every emotion, just as women do, whether or not they have been trained to identify and recognize them. How they express them is often limited by societal or familiar pressure, and far too many men are trained to keep most emotions to themselves. These same men are not trained how to deal with the powerful emotions that they do feel, and many channel them into bullying, aggression, malice, and vengeance, both physical or mental.
Secondly, like it or not, many women are simply not attracted to men who express their negative emotions in the same ways women do, or will lose respect for those who do. Belka touched on this earlier; it's not a societal norm so much as a biological reality.
So what's the answer? Men, deal with your strong emotions (especially those in the realm of fear, sadness, or hurt) privately with God, or with other trustworthy men. It's better not to deal with them with your female partner (and definitely not with a woman other than your partner!). Instead, once you have dealt with them, you might share that you felt a certain way, but share the existence of the emotion, rather than expressing the emotion itself. Also, learn how to deal with powerful emotions in the moment, saving the 'dealing' for an appropriate time.