Immune response to foreign protein
The complexity of the immune response requires foreign proteins to be bound first by presenting cells which happen to be like macrophages - cells that are like garbage disposals. Why some proteins are simply gobbled up and yet others are preserved and presented to the resident T cell helper population is related to the size and sequence of the protein. In other cases, even small molecules (allergens) can bind to native normal proteins and make them look abnormal.
The use of immunoglobulin (semi purified blood) was used in treating certain diseases in the past. These sera were usually developed from animals purposely infected with the disease. Though these proteins also elicited their own immune response (side effects) the kinetics of that event was days to weeks whereas the binding of the immunoglobulin to its target(the virus protein) is a first order event occurring in minutes. Clearance of that antibody antigen complex over hours to days Avoids the catastrophic exponential growth of the virus by keeping the numbers low. Eventually tho side effects WILL happen if you keep giving the serum