The Sanskrit prefix ati, or “excessive,” indicates affection or attachment in which there is no Kṛṣṇa consciousness. Lord Kṛṣṇa says in Bhagavad-gītā (5.29), suhṛdaṁ sarva-bhūtānām: the Lord is the eternal well-wisher of every living being. The Lord is so affectionate that He sits in the heart of every conditioned soul and accompanies him throughout his endless wandering in the kingdom of māyā, patiently waiting for the conditioned soul to come back home, back to Godhead. Thus the Lord makes all arrangements for the eternal happiness of every living entity. 
The best way for anyone to show compassion and affection for all living beings is to become a preacher on behalf of Lord Kṛṣṇa and assist the Lord in reclaiming the fallen souls. If our affection or attachment for others is based on bodily sense gratification, in the name of society, friendship and love, that excessive, unwanted affection (ati-sneha) will cause burning pain at the time of the breaking or destruction of the relationship.
Lesson to be learnt from Foolish Pigeon: http://sastracaksu.nlitn.in/lesson-from-pigeon/
Courtesy: https://www.vedabase.com/en/sb/11/7/52
