Iraq's second-largest city is currently under the control of the Islamic State of Iraq and Syria (ISIS… or ISIL… or the Islamic State… or the caliphate… or Whatever-the-H***-You-Want-to-Call-the-Sunni-Extremist-Messiness).
It's not all that crazy that Mosul was bombed. What is kind of crazy is that nobody is sure who decided to start bombing Mosul.
In most wars, it's a given that you can figure out who is trying to bomb something — even if the country bombing things doesn't really want to fess up to it. For example, during the Vietnam War, the US didn't want to announce that it was bombing the crap out of Cambodia and Laos.
But that didn't stop anyone with a room-temperature IQ from figuring it out. The bombs all fell in Cambodia and Laos, so that solves basic questions about targets. People could also follow the line of reasoning that suggested that the huge B-52 bombing raids launched from Guam were initiated by the US, the only country that operated the B-52 and the proud owners of an airbase on Guam.