I was wrong about aliens

For decades now, I've been making this argument that it's unlikely we've ever been visited by aliens. The argument goes like this:

1. The only thing that could set Earth apart from the billions of planets in the galaxy, and therefore make it worth singling out for a visit, is if it had life.

2. The only way of knowing from a great distance that there's life on earth is by receiving radio signals.

3. The farthest any radio signals have traveled from Earth is a little over 100 light years.

4. If an alien civilization could travel at the speed of light, then any aliens who just got here today because of having received our radio signals and disocvering we were here would have to live within 50 light years of us.

5. If there were any civilizations capable of traveling here who lived within 50 light years of us, we would know about them since (1) they would already have radio technology, and (2) SETI has been searching the skies for decades.

6. But we know of no such civilizations.

7. Therefore, there are no aliens sufficiently close to have discovered us and visited us.

8. Therefore, it's unlikely that any aliens have ever visited us.

People have raised a number of objections to this argument, and some of them have some merit, but not enough to convince me that the whole argument is worthless. But recently, I've come to realize that the second premise is just false, and that undermines the entire argument.

There's another way to discover life on distant planets even if there are no advanced civilizations on those planets. It's by looking at star light that passes through the atmosperes of those planets. You can tell the chemical composition of a light source by breaking it up into a spectrum and looking at aborbtion lines. Absorbtion lines are like finger prints because different elements and compounds produce unique absorbtion lines. Living things on earth give off certain chemicals that, as far as we know, aren't produced any other way. If we can discover some of those same chemicals in the atmospheres of distant exo-planets, that would be good evidence for life. And that's what some people hope to do with the James Webb Space Telescope. This means we could discover life thousands of light years away.

Since there's been life on earth for more than a billion years, life could've been discovered here hundreds of millions of years ago, giving an alien civilization lots of time to travel here or send probes here. So I was wrong. My argument doesn't make it unlikely for aliens to have visited us after all. It still may be unlikely, but for different reasons. I'm just admitting that my long time argument is a failure.