Abram instructed Sarai, "Say you are my sister"

[TonyChanYT]

There was a famine in Canaan in Gen 12. Abram took Sarai to Egypt to escape the famine. He instructed her:

13 "Say you are my sister, that it may go well with me because of you, and that my life may be spared for your sake.”

Did Abram tell his wife to lie?

Sarai was Abram's half-sister. The statement was a half-truth or half-lie meant to deceive the Egyptians. It was a lie in heart.

Gill explained:

though it was not putting a direct lie into her mouth, she being his sister in some sense, as appears from Genesis 20:12 yet it was done to conceal truth, and to deceive the Egyptians, and tended to endanger his wife's chastity,

Abram jeopardized his wife's honor.

as well as showed great timorousness in him, and distrust of the divine care and protection of him;

It showed Abram's deficiency of faith in God.

and upon the whole it must be criminal in him, and shows that the best of men are liable to sin, and the strongest believer to fall, and that a saint may fail in the exercise of that grace for which he is most eminent, as Abram was for his faith, and yet fell into unbelief, and through that into other sins; this he said to his wife, and desired her to say on occasion, when she found it necessary: that it may be well with me for thy sake; his life spared, as follows:
and my soul shall live because of thee; his life be safe and secure for her sake, being reckoned her brother, whereas he feared it would be in the utmost danger should it be known she was his wife.

Abram used/manipulated his wife to save his own skin. His scheme worked only because God interceded and worked with sinners like Abram and us.

What was the reason the story of Abram telling Sarai to tell people that she was his sister and not his wife included in the Bible?

It shows that the Bible writers told it like it was. They did not try to cover things up.

Abram would learn to grow in faith in God as he walked with God more and more.