What gives the sponginess of a Chiffon Cake?
Chiffon cake gets its rise from:


The chemical reaction of the baking powder
Expansion of water into vapor
The expansion of air trapped in the batter


Chiffon cake gets a great deal of lift from #3, mostly from egg whites that are whipped and then folded into the batter. If you are not getting a fluffy cake then these are the most common mistakes. 


Not whipping the egg whites enough: The whipping of the egg whites is very relevant, you need enough fluffiness in them to have trapped air bubbles. You don't have to whip them into hard peaks like most recipes say, but you do need to get them at least to soft peaks. I've experimented with this myself and I find halfway between soft and hard is best as if they are too hard they don't always mix well
Losing air when folding: you have to be gentle folding the egg white in, if you are rough with it or overmix it you pop all the air bubbles and then you get a dense cake
Opening the oven too soon: if you open the oven before the cake has a chance to rise and form a solid structure the cake will cool rapidly and you lose a lot of expansion that you won't regain. Do not open the oven until at least 10 minutes after the cake has stopped rising
Under-baking: This is a mistake I made a couple of times, if you under-bake the cake it doesn't form a solid crystalline structure to trap the air, and it collapses. Once I think the cake should be close I use a touch test and listening test to see if it is done. If I hear a lot of crackling from the cake then it's far from done, if I hear several crackles a second but it's not a constant drone of crackling it's getting there, 1 pop per second or less means the cake is done. A tap test also is good, the cake should spring back very well in the absolute center
Not turning the cake upside down: chiffon cakes needs to hang upside down while it cools, this is because it has expanded so much and is so light. Have what you need to do this ready before you take the cake out and turn it over right away, even 30 seconds makes a difference! 


If the cake never rose much then it's 1 or 2, possibly 3 depending on when you opened the oven. If the cake got good rise but then lost it all then it could be 3 (again depending on when you opened the door), 4 or 5. 

Keep trying, chiffon cake is a little tricky but once you get it worked out it's worth it!