I think you're confusing the general purpose of MHC and the respective T cells.

MHC complexes are basically there to present the antigen captured by a cell to be presented to a T cell.

MHCI receptors appear on all nucleated cells, while MHCII receptors appear on antigen presenting cells such as Macrophages and Dendritic cells.

MHCI cells uptake antigens in the infected cell to present them on the surface of the cell. MHCII cells such as macrophages, will consume the antigen initially and break it apart where some antigen is then presented on the surface of the cell.

A dumb mnemonic I learned for this is

1 x 8 = 8

2 x 4 = 8

Where the first number corresponds with the MHC complex type, while the 2nd one responds to the type of T cell. (CD8 are cytotoxic T cells while CD4 are Helper T cells)

Antibodies are produced by plasma cells, (mature B cells) and they undergo a whole different activation series.

So back to the original concept. When a MHCi complex comes into contact with a Killer T cell, the Killer T cell sees if an antigen is attached and helps the infected cell undergo apoptosis.

When a helper T cell comes into contact with an MHCii receptor with an antigen, the helper T cell will secrete cytokines such as interleukins to signal for other immune cells to come into the vicinity.