My dad lives in Seattle. I brought him to Japan. Him and my stepmom bragged they didn't need an umbrella when it was raining. Watched them walk into a store and drip on books and magazines destroying merchandise.
An umbrella is a bit of false protection from the rain as well. It's a nuisance to carry so often given that it will save you only from a mild inconvenience on most days. And as often as not it'll end up being a hindrance as you fight it from being destroyed or carried away by the wind.
That will probably sound strange to people not familiar with Seattle, considering Seattle's reputation as a rainy city, but the truth is that in terms of total amount of rain Seattle is not actually a very rainy city.
Here are some cities that have about the same annual rainfall as Seattle (37.7 in), within 10%:
Austin, Texas (34.2 in)
Buffalo, New York (40.5 in)
Chicago, Illinois (36.9)
Dallas, Texas (37.6 in)
Kansas City, Missouri (39.1 in)
Oklahoma City, Oklahoma (36.5)
I think there are two reasons Seattle gets the rainy label.
1. The Seattle rain is more spread out. Seattle gets its 37.7 in spread out over 149 days. Compare to Dallas which gets its 37.6 over 81 days. The weather stats folks count as day as a rain day if it gets 0.01 in or more of rain.
Seattle's rain is fairly evenly spread among those 149 days. There will be a handful of times each year when there is a brief moment of heavy rain, but for the most part it is a fairly steady light rain.
In most of the other places, it is much less uniform. They get a handful of big rainstorms, and several fairly rainy days, and many "rain days" that are just small amounts.
2. There is no really bad weather in Seattle most of the time. Some of those other cities with similar total rain also like to dump tons of snow on you, or hit you with hurricanes, or temperature extremes.
Take Buffalo. 40.5 in of rain a year, over 167 days. Sounds like a better candidate than Seattle for the title of rainy city (although I haven't looked at the distribution to see if it is spread out like Seattle's)...but Buffalo also dumps 93 inches of snow a year on people. I think anyone cares about rain when they are getting 93 inches of snow.
Putting these together, Seattle has the perfect combination of many days with enough rain for you to think "it's raining", and a lack of anything else that distracts from the rain, so the rain becomes its characteristic weather feature.
So why are umbrellas kind of pointless here? It rains so often that you'd pretty much have to carry the thing with you all the time to keep completely dry. Eventually you'll forget it, and find yourself having to go out in the rain...and you'll find that it is no big deal. The rain is mild enough that unless you are out for a long time you just get a little damp. Damp hair can be a bit annoying, and if you wear glasses those getting wet can also be annoying...but both of those problems can be dealt with by wearing a hat with a brim, and that doesn't require dedicating a hand.
On those handful of times a year when we get an actual intense rainstorm, you can usually just wait it out. They tend to only last a short time, and then go back to the normal mild rain.