From a practical perspective, we use Java because it is cross-platform and widely used, with a vast array of libraries for handling common programming tasks. C++ or Python would also have been reasonable choices, but we chose Java because it is easier than C++ and faster than Python, with a larger assortment of de facto standard libraries (e.g., Swing) than either.
Java is also one of the easiest languages from which to deploy cross-platform software. In contrast to C++, which has a large number of complex platform issues to consider, and Python, which leans heavily on C and C++ for many of its components (e.g., NumPy and SciPy), Java code is compiled one time into platform-independent byte code, which can be deployed as is to all supported platforms. And despite this enormous flexibility, Java manages to provide time performance nearly equal to C++, often better in the case of I/O operations.
Historically, LOCI's software projects grew around efforts to harness VisAD, a Java component library for interactive and collaborative visualization and analysis of numerical data, within our VisBio application for visualization of multidimensional microscopy data. We also added support for several microscopy formats to VisAD before splitting the code into a standalone library, Bio-Formats. The choice to use Java and VisAD (rather than, e.g., C++ and VTK) was partially motivated by the fact that LOCI's lead software architect Curtis Rueden was already an expert on Java and VisAD technologies. Choosing Java also enabled cross-platform integration with ImageJ, one of the most popular freely available image processing tools in the life sciences field, as well as with the OMERO system for visualization, management, and annotation of microscopy data.