My first suggestion is to review the IMBA rules of the trail:
1. Ride On Open Trails Only.
Respect trail and road closures (ask if uncertain); avoid trespassing on private land; obtain permits or other authorization as may be required. Federal and state Wilderness areas are closed to cycling. The way you ride will influence trail management decisions and policies.
2. Leave No Trace.
Be sensitive to the dirt beneath you. Recognize different types of soils and trail construction; practice low-impact cycling. Wet and muddy trails are more vulnerable to damage. When the trailbed is soft, consider other riding options. This also means staying on existing trails and not creating new ones. Don't cut switchbacks. Be sure to pack out at least as much as you pack in.
3. Control Your Bicycle!
Inattention for even a second can cause problems. Obey all bicycle speed regulations and recommendations.
4. Always Yield Trail.
Let your fellow trail users know you're coming. A friendly greeting or bell is considerate and works well; don't startle others. Show your respect when passing by slowing to a walking pace or even stopping. Anticipate other trail users around corners or in blind spots. Yielding means slow down, establish communication, be prepared to stop if necessary and pass safely.
5. Never Scare Animals.
All animals are startled by an unannounced approach, a sudden movement, or a loud noise. This can be dangerous for you, others, and the animals. Give animals extra room and time to adjust to you. When passing horses use special care and follow directions from the horseback riders (ask if uncertain). Running cattle and disturbing wildlife is a serious offense. Leave gates as you found them, or as marked.
6. Plan Ahead.
Know your equipment, your ability, and the area in which you are riding -- and prepare accordingly. Be self-sufficient at all times, keep your equipment in good repair, and carry necessary supplies for changes in weather or other conditions. A well-executed trip is a satisfaction to you and not a burden to others. Always wear a helmet and appropriate safety gear.
I think rule number 4 answers your question. I always announce myself when coming up on other riders/hikers. I try very hard not to startle them since I know I can get startled easily. I do believe that the women I see on the trail are more friendly than then men who blow by without any sort of grunt.



Twice I got as far off the narrow trail (steep incline on one side, drop off on the other) as I could, one time I slipped on the steep embankment trying to get over (and got several splinters in my hand when I caught myself), apologizing profusely each time for my ineptness. The other time I was riding so I sped up as fast as I could for a section until I realized the dude was still on my back tire and I reached a wider spot where I could pull off. One gal thanked me for getting out of her way, the other (men) didn't say anything. They didn't even announce their presence behind me as we are supposed to do when encountering a hiker (if I was off my bike I guess I was a hiker?).
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But these are the people that contribute to the bike bans in certain parks, so they are really ruining it for the rest of us.

So maybe those people suddenly appearing behind you, or swooping past without a sound aren't being arrogant, they might just need all their focus to get through the section.
