In parades it is what they have been doing since ages and they are trained to do that.
Now comming to the point of them pointing it upwards in other situations like operations i think earlier there was no particular rule or code as to how to hold the weapon so everyone held it in a position they were more comfortable in..not that they didnt have the trigger discipline but still in a position that suited them most.
But since 7-8 years i have been seeing a change in training where everyone is getting trained specially in the Army to keep the gun barrel pointing downwards(foreign army type) and nowadays you would hardly see a infantrymen pointing his barrel upwards.
Since you have asked i want to take this oppurtunity to highlight a few more things..I also used to wonder the same thing among others like why are our troops not trained in advanced room intervention techniques..why do only two soldiers do room intervention drills in the Army in buddy pairs?..why doesnt the IA use the sniper extensively?..why doesnt the IA SF carry a secondary weapon etc.
But these things have been changed in the last few years and IA is investing a lot in training.I have seen the Army all my life since the early 90s and never have i seen the training in the Army change as much as i have seen in the last 7-8 years.
Morever upwards or downwards doesnt matter as long as the barrel is not pointing towards someone but yeah pointing it downwards looks more professional and cool.
(i hate it when they keep it on their shoulders)
I have been watching a lot of US Seal videos in the past few months and i have noticed that in their room intervention technique just before entering a door they keep the barrel pointing upwards.
Different units have different techniques!