Because you can argue that if your cross-price elasticity is positive relative to another product,you then do not possess any exclusiveness to the product.
In another word,being a monopolist,you possess market power,this is mainly because you are selling a exclusive good,that there is no where else the consumer can get it from.
So if you rise your price,some consumer may leave,but the others will stay.
However,if it is the case that the price elasticity of demand of your product is positive compared to other goods,that is,if you rise your price by 1 percent,the demand of a second good increases by a certain percentage,then it must be true that there exists other firms or company that sells goods which could potentially replace your product,then you are no longer a monopolist since you dont produce an exclusive good.
This is why you could use cross-price elasticity of demand to determine whether a firm is a monopolist
BTW:dont use what i just said for your exam,its just too casual,take the ideas and build up on it.ECON111 is boring,im off to ACST211 hope i did help you.