This topic is treated in most books and sites so I've tried to explain it to you in a more unusual and friendly way to grasp the concept but maybe the canonicals explanations are more suited for exams and serious conversation.
First step idealize and simplify the Raoult law
You can see Raoult law as the most basic attempt to predict the partial vapour pressure of a multi-components solution. If $A$ is your first component with higher vapour pressure an $B$ is the second component with lower vapour pressure, it seems quite obvious that if you mix an equal amount of $A$ and $B$ you have a vapour pressure equal to the mean of the two.
Back to reality
In fact, the reality is more complex and you have to take into account the force between the molecules of the two components. If you have strong adhesive forces the molecules of the first component near the molecules of the second keep themself more stuck together. So this creates a sort of "net" that doesn't allow the molecules to "escape" from the solution and so the vapour pressure (that in fact quantify the ratio of molecules that "escape" from the bulk) is lower and finally you have a negative deviation.
But what if the interaction between the molecules of the same component is greater than the interaction between the two components? As you state, this is the case of strong cohesive forces. In this case you have to imagine that the components act as if they were separate. Molecules of the component A lower the positive interaction between the molecules of the component B interposing them self and avoiding the formation of bonds between molecules of component B and finally increasing the vapour pressure, a positive deviation!
Deep into fantasy
So if you think the molecules as humans exiting from an elevator, humans A are more claustrophobic and so tend to exit more rapidly than humans B when the doors open. If they interact positively with humans B they will keep calm when exiting. If humans B don't find funny humans A they preserve their panic attitude and at the same time separate B humans from each other and rushing out from the elevator pull humans B out more rapidly too!