I will argue that not everyting happens for a reasons, as follows.
Many things happen for reasons. When I pour water into a glass in order to drink it, the water entered the glass for a reason. Namely, it entered the glass in order to quench my thirst. But, it only did so because I made it do so. In this case, the reason I pour the water into the glass is for my own benefit.
Other things happen for reasons, which do not benefit the person takes the action. For instance, if I jump into a pond to save a drowning child, the movement of the child from the pond to dry land happens for a reason. But, the does not involve my own benefit, but the child's. So, this is a non-self interested reason.
Other things happen for reasons that benefit no one. I may simply decide that I want to kick a rock on the pavement, as children sometimes do. This benefits neither me nor anyone else. But, it still happens for a reason. In this case, the rock moved from one part of the pavement to another simply because I had a desire to kick it at the time. This may seem like a trivial reason, but it is still a reason.
What all of the above events have in common is that they are undertaken by people (or, more specifically, "reasoning agents"). What about actions that are not caused by people? I think it's hard to see how these kinds of actions could happen for a reason. It's true that events that are not caused by people may still have causes. For instance, a rock might fall to the ground because gravity caused it to fall. But this isn't a reason, in the sense that we normally use the term. Consider my glass of water again. If natural causes were reasons, then we might say that the reason the water entered the glass was because gravity put it there. But this is not what we mean when we want to know the reason why there is water in a glass. The reason is that I put it there. gravity is only part of the cause, rather than a reason.
So, events that are not caused by rational agents do not happen for a reason. Therefore, not everything happens for a reason.
What if you believe in a supernatural agent who is the cause of all events? Then, perhaps everything does happen for a reason. But, then you have to argue for the existence of such an agent, which is difficult to do. We would also have to amend the way we normally talk about reasons. If God is the cause of all events, then the reason why I poured water into the glass was not because I was thirsty, but because God willed me to pour water into the glass. If we don't want to amend the way we talk about reasons, perhaps conclude that God's will does not constitute a reason. In this case, we would be back to where we started; not all events happen for a reason, even if they are all willed by God.
The phrase "everything happens for a reason" is often used to provide consolation. However, even if everything happened for a reason, that would be no consolation in itself. Many people do things for bad reasons. The holocaust happened for a reason (i.e. because Hitler wanted to eliminate the Jews), but the reason was a very bad one. So when someone says "everything happens for a reasons" in order to provide consolation, we should really take them to mean "everything happens for a good reason." This claim is very implausible. I just provided one example of something that happened for a very bad reason. One can think of many other examples.
So, not everything happens for a reason, assuming there is no supernatural agent that is the cause of all things. If there is such an agent, then perhaps everything happens for a reason, but if we accept this we also have to accept that a lot of the reasons we normally ascribe to events are actually false. Although "everything happens for a reason" is often used to provide consolation, it should not provide consolation, since there are bad reasons. It is not the case that everything happens for a good reason.