Another aspect of the mitzvah is not so much about the bird as it is about the person chasing the bird away. Rabbi Wallerstein takes his children to feed the birds in the park before Shabbos. The primary reason for this is not to help the birds but rather to instill a behavior and attitude of kindness in his kids.
Chessed (kindness) is not an inherent trait in humans, it must be cultivated thru behavior.
Kindness towards animals is an example of pure chessed. The animal can not knowingly repay you and often the animal is not even cognizant of the kindness you have done. Kindness towards animals is a great way to develop a Chessed worldview.
Rav Yehudah Ha Nasi suffered from stomach pains because a goat was being lead to the slaughter and hid under his cloak, he instructed it to go for that was its destiny. 13 years later his maid was cleaning his house, getting rid of some mice, he instructed her to be gentle because they were babies, only then his stomach pains ceased.
Chessed is not something you do at certain points during your week. Chessed is developing a sensitivity to the world around you. Man is the only animal capable of such behavior, through contemplation and more importantly through action. Developing this perspective is one of the objectives of the Torah.
Further Parsha study.
In this weeks Parsha several allusions are made to indviduels from Berashis . Can you find the pasukem that reference: