Why are antibodies Y-shaped?
Antibodies also known as immunoglobulins consists of two heavy chains and two light chains linked via disulfide bonds to form Y-shaped structure (as shown in figure below).
This Y-shaped structure bestows antibodies with two properties. Firstly, antigen-binding through the antigen binding fragment(Fab); and secondly, interaction with immune cells and proteins through fragment crystallizable region (Fc) to stimulate and regulate host immune defense mechanisms.
Fc and Fab portions of the antibody molecule are joined by flexible hinge region which enables antibodies to interact with the antibody-binding proteins and thus help in mediating immune effector mechanisms. So, this Y-shaped structure provide proper flexibility for binding to antigens and proteins/immune cells of immune system.

Reference
https://www.ncbi.nlm.nih.gov/books/NBK27144/
https://immense-immunology-insight.blogspot.com/2013/10/antibody-structure-simplified.html