Because he had realized the superiority of prema, his goal, over realization of the bliss of brahman, he taught Bhagavatam to Suka so that he also could see the superiority of the bliss of prema. In this world, if the father has experienced something blissful, he will attempt to have his son experience this also. That is explained in this verse.

First Vyasa had made an abbreviated scripture about bhakti, but on the advice of Narada, he rearranged it (anukramya), purified it, giving most prominence to bhakti to Krsna.

Narada gave his instructions after the disappearance of Krsna and before Pariksit punished Kali, because at that time itself there was a tendency towards irreligion even among the followers of religion and adherents of scripture since the power of Kali manifested even at the beginning of his control. Because of this, Vyasa was dissatisfied in his heart. This is shown in the following verse:

jugupsitam dharma-krte ’nusasatah svabhava-raktasya mahan vyatikramah
yad-vakyato dharma ititarah sthito na manyate tasya nivaranam janah

You have created a great disturbance by teaching what is condemned to people attached to material enjoyment in order make them accept dharma. Thinking that what you have taught is real dharma, they do not consider giving it up. SB 1.5.15

It is understood that before the beginning of Kali-yuga he would not have been dissatisfied in heart. Now at this time, he revised the Bhagavatam which was previously written. When it is said krsne svadhamopagate, ... purano ’rkto ’dhunotditah (SB 1.3.43), this refers to the revised Bhagavatam, the present one. EWhen it is said that the present Bhagavatam is another Bhagavatam and that the Bhagavatam is among the eighteen Puranas, it refers to the same Bhagavatam, the present one... Nivrtti-niratam means that Sukadeva had realized brahman.