By default, anchor tangents are unbroken so that if you move one tangent, the tangent on the opposite side moves accordingly to keep them aligned. This keeps the curve smooth.
You can break a tangent manually to create sharper corners on your curve.
To break the tangency of an anchor
Alternatively you can select a tangent and select Edit Curves > Bezier Curves > Tangent Options > Break Anchor Tangents. You can also break a tangent in the Bezier Curve Tool by + dragging a tangent.
You can create corners with or without tangents using the Corner option.
Maya breaks the tangents of the selected anchor and repositions them toward adjacent anchors.
Alternatively you can select a tangent and select Edit Curves > Bezier Curves > Anchor Presets > Bezier Corner or Edit Curves > Bezier Curves > Anchor Presets > Corner.
You can smooth broken tangents so that they move together resulting in smooth curves.
Maya straightens the tangents based on what you selected. Now if you move one tangent, the other moves with it to preserve their alignment.
Maya smooths the tangents and sets them perpendicular to the anchor’s normal. The tangent lengths are the average of the original tangents.
Alternatively you can select a tangent and select Edit Curves > Bezier Curves > Tangent Options > Smooth Anchor Tangents or Edit Curves > Bezier Curves > Anchor Presets > Bezier.