Why are planes using rivets & not welded construction?
Short answer: High-strength aluminium alloys are tricky to weld correctly. Aluminium is such a fine material for aircraft structures that the need to rivet it is gladly accepted.
Two things are important:

While steel has a temperature range in which it gets more and more runny, aluminium alloys change from solid to liquid within a few degrees. Also, heat conductivity in iron-based alloys is lower than in aluminium, so heating steel locally will keep the surrounding material cooler and more solid compared to aluminium. While welding thin sheets of steel is trivial, it needs lots of experience in aluminium. For very thin sheets, special equipment like a water-cooled copper backing on which the aluminium sheets rest, so their back is cooled, are needed. Also, the melting temperature of steel and titanium is high enough for it to glow long before it melts, while aluminium will melt without giving you any optical hint of its temperature.

High-strength aluminium is produced by progressively aging and precipitation hardening the material. The usual alloys use copper atoms dispersed through the aluminium matrix which locally distort the atomic lattice and strengthen it. If they are heated and rapidly cooled by welding, the copper distribution would be changed and the material would be weakened around the welding area. To harden the finished structure again is rather impractical in most cases, so riveting is the better alternative.


A third speciality is the oxide layer on aluminium, which has a higher melting temperature than the base material. You need an AC TIG welder to disrupt the aluminium oxide layer, so your choice of welding techniques is rather limited.
Also, riveted structures are easier to inspect and to repair. Most repairs need to remove aircraft structure for access, and a riveted structure is easier to disassemble and to put together again after the repair using slightly thicker rivets.
My experience with aluminium welding stopped at 4mm thick sheets; while thicker ones were easy to weld, I never managed to weld thinner ones. You sit in front of your structure and heat the spot where you want to start welding. Watching it through the darkened head screen you wait until the spot under the arc becomes glossy, which signals that the surface has started to melt. Now you need to add your welding wire like crazy to keep the spot from heating more, and get the spot moving. If you fail to do so, a second later you will have a hole under your arc, because the aluminium has molten completely and has fallen away. Doing this with 2mm sheets was a pure exercise in futility for me - the moment the surface became glossy it fell away already.


Edit:
Thanks to @voretaq7 for sharing the link about friction stir welding in the comments! This is made possible by precise positioning of the parts and a computer-controlled welding head and will see wider application in the future. Eclipse Aerospace claims it helps them to avoid 60% of rivets in their jet aircraft.