The maximum matching problem is one of the most fundamental algorithmic graph problems and OBDDs are one of the most common dynamic data structures for Boolean functions. Since in some applications graphs become larger and larger, a research branch has emerged which is concerned with the theoretical design and analysis of so-called symbolic algorithms for classical graph problems on OBDD-represented graph instances. Typically problems get harder when their input is represented symbolically, nevertheless not many concrete non-trivial lower bounds are known. Here, it is shown that symbolic OBDD-based algorithms for the maximum matching problem need exponential space (with respect to the OBDD size of the input graph). Furthermore, it is shown that OBDD-representations for undirected graphs can be exponentially larger than OBDD-representations for their directed counterparts and vice versa.