Arguably the most important factor in Leonardo's interest in anatomy was Andrea's urging for all of his pupils to have an excellent grasp of it. Leonaro's apprenticeship, however, would have begun not with immediate collaborations with his teacher, but instead with simple chores like preparing canvasses. In the process, the importance of anatomy in painting, along with many other technical skills, was likely impressed upon him.

Many of the new painting techniques of the Rennaissance can be seen in Verrocchio's work, including the use of perspective in backgrounds, heightened through atmospheric distortion and sfumato. It may also be noted that Leonardo was fond enough of Verrocchio to continue collaborating with him even after the former had his own workshop.

Sources:
"Leonardo da Vinci." https://en.wikipedia.org/wiki/Leonardo_da_Vinci. Accessed 8 Mar. 2018.
"Andrea del Verrocchio." https://en.wikipedia.org/wiki/Andrea_del_Verrocchio. Accessed 8 Mar. 2018.

Image source: https://www.pubhist.com/w21323