When speaking of attachments, desires, cravings, etc., people often seem to focus on positive things: love of/for pleasure, family, friends, a certain place, etc. However, attachments can also be negative. For example: an activist might hate corruption or injustice, a police officer might hate crime or criminals, a military officer might hate foreign aggressors, a terrorist might hate another religion or ethnic group, an abused person might want revenge, an abusive person might want to exploit others, a corporate boss might want to conquer every competitor, a politician might want dictatorial power, and so on. Of course, most people probably have a mixture of positive and negative attachments.
As I understand, in Buddhism, rebirth happens because of any attachment to this (or any) world, not only positive attachments. The Buddha also seems to have been attached to “the pleasure of renunciation, the pleasure of seclusion, the pleasure of peace, the pleasure of self-awakening” (AN 8.86), which are perhaps attachments leading to nirvana.