This topic is treated in most books and sites so I've try to explain it to you in a more unusual and friendly way to gasp 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 vapor pressure of a multi components solution. If $A$ is your first component with higher vapor pressure an $B$ is the second component with a lower vapor pressure, it seems quite obvious that if you mix an equal amount of $A$ and $B$ you have a vapor pressure equal to the mean of the two.
Back to reality
In fact the reality is more complex and you have to take in 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 them self more sticked together. So this create a sort of "net" that doesn't allow the molecules to "escape" from the solution and so the vapor 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 vapor 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 than humans B. If they interact positively with humans B they however calm them self and exit with calm. If humans B don't find funny humans A they preserve their panic attitude separate B humans from each other and rushing out from the elevator pull humans B out too!