Because of the cation sizes; the A position is assumed by cations having larger radii like Ca2+ (100 pm), Sr2+ (118 pm), while the B position is occupied by Ti4+ (60.5 pm, that is about 40% smaller) or similar cations, all coordinated by O.

The explanation given by Gavri Sabau is not totally right. In an ideal perovskite structure a perfect octahedral position B can be occupied only if the cation is 0,414 times the ionic radius ox the oxygen anion, which is 140 pm (or 1.40 Ansgtroms) = 58 pm, So Ti is a little larger than that and tends to enlarge a bit the side of the cell where it is located. Instead, very few cations can occupy without a severe structural distorsion the "A" site, in 12-fold coordination or cubo-octahedral corrdination.  Not even Ba is a large as oxygen, since this "A" site really means that a cation is large enough to susbtitute for an oxygen in the center of opposite faces in the FCC cell. But both cations A and B, are NOT next to one another, to minimize electrostatic repulsion the Ti lies in a plane running trhough the center of the cell, occupying the edges  away from the faces occupied by the larger A cations. No perovskite structure has a tolerance factor of exactly 1, in particular the mineral perosvkite itself is not a perfect cubic structure, and has 0,707 < T < 1. and it tends to deform the cell giving an orthorombic or even monoclinic symmetry, pseudo.cubic is called, as the crystal faces "look" like cubic or octahedral. If T is equeal or less than 0,707 the structure adopted must that of ilmenite, a derivative structure of corundum, where both cations A and B are in octahedral coordination and oxygen forms an HCP (AoBoOh3). The Lima-de Faria model structure for perovskite can be rewritten as: AcBoOc3, thus the complete FCC cell has one cation A (1/2 X 2) located in opposite faces) plus three oxygen cations (2/4 x 4) located in the remaining centered faces + (1/8 x 8) located in the edges or vertices of the cube, a total of 1 A and 3 O,  and of course (1/4 x 4) B cations, located in only the center of four sides of the cell, in octahedral coordination.  Taken all this in consideration it is easy to see why the A-O bond lenght is 40% (or so) greater than the B-O bond lenght. Perovskite is a fascinating structure, most of the lower mantle of Earth is composed by bridgmanite, a polymorph of enstatite with a perovskite structure, adopted because of very hugh pressure conditions: MgcSioOc3. In this structure, Si occupies the octahedral sites and Mg the cubo-octahedral positions, this means that the ample electronic shell of oxygen is shrunk at least 30%, as to lower its ionic radius, so that the cations are relatively larger. A similar effect also happens in the cation electronic shell, but in a smaller proportion, no more than 5%. Therefore the ionic radius relation increases for both cations and Si occupies (o) sites instead of the familiar (t) sites, and Mg occupies cubo-octahedral sites, instead of the normal (o) sites, as in enstatite, olivine and other mafic silicates.