You didn't cause the accident. However, you might have been wrong to slow down. I don't know where you live or exactly what the circumstances were, but this is extremely common in the US, where people don't really know how to drive.

It's ok to let someone out if:

* they are waiting at a 1-way stop sign or uncontrolled junction

and

* traffic on the other side has stopped or slowed, so you are going to have to stop or slow down anyway. In that case, it's polite and efficient to let them out.

Otherwise, barring some unusual circumstance, you should proceed. When you have the right of way, and it's safe to go, then go - that's the rule. Forcing everyone else to slow down or stop so that you can let someone out is not courteous or polite. And, as you have seen, there may be people who are not required to stop, and who are not parties to your little arrangement with the other driver. You would fail a driving test (in any country that has a serious driving test) if you make a habit of this.

I want to reiterate that this doesn't make the accident your fault - and it may have been perfectly reasonable for you to slow down; I wasn't there.

In the UK, we're told that if someone let's us out, we should always look first to make sure nothing else is coming. Just because you allowed them to pull out doesn't mean you told them it was safe to do so, and they should have still looked to ensure it was safe to pull out.

I agree with your wife and don't think you caused the accident. It was their fault for not being more aware of their surroundings.

> I'd like some advice on how to cope with this

Lay low and pray no one escalates the matter into a frivolous lawsuit, although the incoming driver is clearly at fault. Continue waving people in when slow traffic conditions warrant, as this is a very normal and nice thing to do.

> my action directly lead to a fellow human getting hurt.

INdirectly, and not even that. If she had been a few seconds behind where she was now, you hadn’t stopped, he waited for a few seconds to let you pass and then hit her, would you feel guilty, too?

I am still haunted by the time I was in Washington DC walking with some coworkers from LA and one of us stepped in front of a car at Union Circle, the car brakes, and the car got rear ended by another car.

Seems to me what you described is a cyclist passing on the inside or traveling in the wrong direction if there was time for the other driver to wave thanks! This would put the responsibility squarely on the cyclists shoulders. Chances are, if there was an exchange between the cyclist and the other car's driver, the car owners insurance will pay out unless you recorded their license plate number and notify your local authority as a witness, but it sounds to me like you believe the cyclist is the victim so IDK.

I was always taught to never wave or otherwise indicate to another driver to proceed but slowing down is fine, and never ever ever EVER act upon the invitation or waiving from a pedestrian to proceed(Such as a person waiting at a crosswalk that you stop for that waives you to go) as the person in the vehicle is always in charge of that situation. I know this was not your situation but feel it is relevant enough to mention.