Dogs exhibit aggression for several reasons. There is a difference between the aggression against people and the aggression toward other animals. Beagles aren't especially aggressive dogs but they do have instinctual behaviors.
If your beagle displays aggressive behavior toward you or any family member it's his way of expressing that he feels the object of his aggression is lower in the pack pecking order than he is. This behavior might be snapping or snarling over food or toys or refusing to get off the sofa. It is any behavior that shows him to be questioning the authority in any way.
In the natural pack life of dogs no other dog ever questions or challenges the alpha dog in any way. He is the absolute ruler. Only when he shows weakness that could mean he isn't fit or capable of leading is he challenged.
In other members of the pack aren't resentful or angry about this arrangement. On the contrary, they have the assurance and comfort of a strong leadership to act in the pack's best interest.
In your household there is room for only one leader and if you don't want your life run by a Beagle you need to show the characteristics of an alpha dog to keep your place in the pack.
One easy thing is not to allow your Beagle on the furniture. The simple factor of height will help establish your ranking. Never allow him to sleep on your bed. For humans this may be an act of affection and fun but to dogs it means dominating you and taking over your sleeping spot. Give and take attention and affection on your terms and not his.
Don't react to his aggression or dominating behavior with aggression of your own. Instead apply the same principle an alpha dog would use and simple ignore him completely.
The alpha dog knows that he's above petty squabbling and ignores it unless it gets out of hand. Your dog will recognize this and return to you the respect you deserve.
Remember when your dog shows this dominating or aggressive behavior it is indirectly your fault for having forced him to the decision that he needs to take over for the good of the pack. If he actually becomes aggressive enough to pose a danger, please seek the help of a professional trainer to deal with what can be complex issues. An aggressive beagle can be trained.
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people and the aggression toward other animals. Beagles aren't especially aggressive dogs but they do have instinctual behaviors. 
