Is it cruel to keep birds?

I would love a budgie, we would have three or more and they will be in a big and I mean big aviary. It will have a double door and we can walk inside it and move around. They we be well cared for, we will take them out and play with them and train them and we would never clip their wings. I just think they are amazing creatures and I would love one and so would my dad and brothers but my mum keeps saying birds should be free. Should the be free? Also can you let homing pigeons fly free during the day and put them in their loft at night, my mum would warm up to that idea