It is entirely possible to be in love and independent. In fact, someone who is independent in love will love everything, and not just selectively their own clan, circle, or possessions.

ṣvaṅga in the word anabhiṣvaṅga represents clinging to what is dear and being emotionally entangled with it. An- is its negation. Abhi expresses an intensification, a growing attachment.

This is the crux of many human, worldly problems. People are focused on their own group, thus separating themselves from the outside, with all the xenophobia and hostility that entails. Current world events speak volumes.

Regarding preparation for freedom. Attachment to son (putra) or daughter (putrī), wife (dāra) or husband (pati), or home (gṛha), as mentioned in Bhagavad Gītā 13.10 (anabhiṣvaṅgaḥ putra dāra gṛhādiṣu), somehow hinders my focus on the infinite love of myself. I must do my dharmic duty, and therefore dutifully care for what I karmically need to care for. But for pure self-enquiry, I must look closely at the source of the worries that possessions, parenthood, or partnership often evoke. These are powerful forces in the self-enquirer. Worry is always unwarranted, because īśvara cares for everything. Often we only disrupt the other person’s (the loved one’s) chance for self-care, on the ultimate path to freedom.