It seems to be that there are certain monsters that have the somewhat unnerving ability to follow your character around. The first time it happened to my, I was a lvl 6 Thaum running around Gridania and I heard the pitter patter of feet behind me. I spun around and there was this Canopy Galago coming at me. To me there were a Red Icon mob so I thought it was agro and rushing up to kill me, so I yelped and started running, only to have it keeping on following me. I managed to escape it and considered myself lucky until I realised that it wasn't really agro. I know in Limsa, the Dodos can follow like pets and I've had a Copper Coblyn follow me in Ul'Dah.
Any thoughts on why these mobs do this? Or got any stories to share about a 'pet' you've encountered?