Catalyzes the cleavage of L-allo-threonine and L-threonine to glycine and acetaldehyde. L-threo-phenylserine and L-erythro-phenylserine are also good substrates (By similarity). L-threonine = acetaldehyde + glycine L-allo-threonine = acetaldehyde + glycine Homotetramer. Belongs to the threonine aldolase family.