From its architectural point, if you thought it's symmetry was the most peculiar thing, you are wrong. If you thought it not, you are further wrong!
Every piece in the Taj , including those trees, once lined its garden were done with symmetry. There is even this massive structure built in the complex , called Jawab (literally means 'answer' to match the mosque in the garden next to Taj.
The tomb of Mumtaz Mahal is at the very center of this symmetry. It has to be... Mumtaz was the very reason for Taj.
So many years later, when Shah Jahan's tomb had to be built, and that too next to the tomb of Mumtaz , there was no choice but to break the symmetry for the first time in its design!
See also the Poor man's Taj!