I think the main problem with agreeing whether love does or doesn't exist is simply the fact that everyone tends to view the concept of love differently. For example, Candians and American equally treasure the concept of freedom, but their concept of freedom fundamentally differs:
Canadians support a "postive" freedom where state intervention is necessary to permit the lower economic strata the "freedom to develop"
Americans (keep in mind these are simply generalizations) support a "negative" freedom, or a freedom from restraint: meaning the state interferes in their lives at a minimal level.
Where's the parallel?
Some people view love as a chemical response to ensure the survival of our genetic code, others view it as going "head over heels" or that they simply just "feel it" (by caring so much about one person to an almost unfathomable degree).
Conclusion: I think it would be difficult to declare that love as a broad concept does not exist. This is because people often define love according to their past relationships, i.e. "love is what I felt with (enter name here)". So, if you believe you're in love, you're in love (and vice versa).
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