Krishna says in the Bhagavad Gita that he is Samaveda among all the 4 Vedas. Why did he specifically

As far as I can understand from Srila Prabhupada’s explanation below, the Sama Veda is special because it contains the Brihat-sama, and various other beautiful songs by the demigods.

Krishna says:

Of the hymns in the Sama Veda I am the Brihat-sama, and of poetry I am the Gayatri. Of months I am Margasirsa [November-December], and of seasons I am flower-bearing spring. —Bg 10.35

Srila Prabhupada explains:

It has already been explained by the Lord that amongst all the Vedas, He is the Sama Veda. The Sama Veda is rich with beautiful songs played by the various demigods. One of these songs is the Brihat-sama, which has an exquisite melody and is sung at midnight.

In Sanskrit, there are definite rules that regulate poetry; rhyme and meter are not written whimsically, as in much modern poetry. Amongst the regulated poetry, the Gayatri mantra, which is chanted by the duly qualified brahmanas, is the most prominent.

The Gayatri mantra is mentioned in the Srimad-Bhagavatam. Because the Gayatri mantra is especially meant for God realization, it represents the Supreme Lord.

This mantra is meant for spiritually advanced people, and when one attains success in chanting it, he can enter into the transcendental position of the Lord. One must first acquire the qualities of the perfectly situated person, the qualities of goodness according to the laws of material nature, in order to chant the Gayatri mantra.

The Gayatri mantra is very important in Vedic civilization and is considered to be the sound incarnation of Brahman. Brahma is its initiator, and it is passed down from him in disciplic succession.

The month of November-December is considered the best of all months because in India grains are collected from the fields at this time and the people become very happy.

Of course spring is a season universally liked because it is neither too hot nor too cold and the flowers and trees blossom and flourish. In spring there are also many ceremonies commemorating Krishna's pastimes; therefore this is considered to be the most joyful of all seasons, and it is the representative of the Supreme Lord, Krishna.