Why is sheep erythrocyte lysis considered as classical complement activation pathway, and rabbit as alternative one?

The sheep erythrocyte lysis you mention actually involves sensitised erythrocytes, i.e. erythrocytes already coated with antibodies. Antigen-antibody complexes are well-known for their activation of the classical complement pathway.

In fact, rabbit erythrocytes coated with antibodies also activate the classical complement pathway$^1$. Thus, sheep erythrocytes are not special in this regard.

The difference comes when we incubate only erythrocytes—devoid of any sensitising antibodies—with serum containing complement factors. In this situation, erythrocytes from the rabbit, but not those from the sheep, are lysed by alternate complement activation. Why is there such a difference?

Fearon and Austen$^2$ showed that this is due to a protective effect of the rabbit erythrocyte membrane on C3b. Normally, C3b is inhibited by factor I and factor H in serum. This effect is lost with rabbit (but not sheep) erythrocytes, which explains the difference in complement-mediated lysis.

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Journal articles cited:

1. Dijk HV, Rademaker PM, Willers JMN. Estimation of classical pathway of mouse complement activity by use of sensitized rabbit erythrocytes. Journal of Immunological Methods. 1980 Dec 22;39(3):257–268. https://doi.org/10.1016/0022-1759(80)90060-5
2. Fearon DT, Austen KF. Activation of the alternative complement pathway with rabbit erythrocytes by circumvention of the regulatory action of endogenous control proteins. Journal of Experimental Medicine. 1997 Jul 1;146(1):22–33. https://doi.org/10.1084/jem.146.1.22