  A group is $\frac{3}{2}$-generated if every non-identity element is contained
in a generating pair. A conjecture of Breuer, Guralnick and Kantor from 2008
asserts that a finite group is $\frac{3}{2}$-generated if and only if every
proper quotient of the group is cyclic, and recent work of Guralnick reduces
this conjecture to almost simple groups. In this paper, we prove a stronger
form of the conjecture for almost simple symplectic and odd-dimensional
orthogonal groups. More generally, we study the uniform spread of these groups,
obtaining lower bounds and related asymptotics. This builds on earlier work of
Burness and Guest, who established the conjecture for almost simple linear
groups.
