Negative liberty sounds like the ideal way to realize liberty for each individual. Taking away any interference would mean a person could do whatever he or she wants.
The reality is that too much negative liberty means either isolating yourself or taking away the liberty of others.
For instance, what if that ‘interference’ becomes the other individual’s liberty? Whose negative liberty would be more important, yours or the other’s? Negative liberty alone does not offer solutions for inter-individual conflicts, other than severing communication between those individuals. But that would mean taking away the (social) liberty for those individuals to be able to interact. So in the end, if everyone gets all the negative liberty they want, everyone loses, or ends up alone.
Too much positive liberty is not good either. That would mean liberty would be a prescription, rather than a preexisting condition, which means liberty would be artificial and liberty would not be authentic and therefore not free.
However, offering negative liberty exclusively as the gospel of all liberalism (or should I say a specific branch of liberalism) would mean the deconstruction of society itself, isolating everyone from each other or either letting one steal the liberty of the other, instead of realizing the presumption that differences would find their place if everyone would have as much negative liberty as possible. There will always be the need for some positive liberty to ease conflicts between the liberty of two or more individuals and offer a solution for the paradox that an individual with all the negative liberty in the world would not have individual liberty, but individual dictatorship, and take away all his or her own social liberty, as individuals could not have the opportunity to socially develop themselves. Then, not the state would be a threat to liberty, but the individual itself.
Too much negative liberty for one individual would mean less liberty for other individuals. Without realizing this, liberalism would be the enemy of itself. It works like magnets; having both a negative pole means the magnets push each other away, and both having a positive pole means the magnets push each other away again. Having one with some of the negative and one with some of the positive causes them to attract each other and the magnetism is complete. Without having the power and the resources, the liberty of an individual would be limited to his or her predisposition. Without having a defense against interference, the liberty of an individual would be endangered by external influences. However, with the power and resources to be free and ways to deal with interference, the net result would be even more liberty.