I've not read any of the (many) replies to the original question, so forgive me if this is redundant, but other than the Nike slogan ("just do it"), I suggest picking a section of trail and a time of week and year where you expect a good few other hikers coming by. This will both increase your actual safety by some unknown margin as well perhaps as help your psyche. I.e., if you don't stray far off trail, you know that someone is likely coming along in the not too distant future who can perhaps help out if you get into some situation you can't handle alone.

If loneliness is a concern, an MP3 player packed with music and/or audiobooks can help, though I think that unless you're on quite a long trip it's very nice to just have some extended "alone time". It can be difficult in normal life to have that, to touch base with yourself and see how well you and yourself get along so to speak. Hopefully the results aren't alarming.

I find that when I'm with a group I miss hiking solo sometimes, and when I'm solo I on occasion miss hiking with a group. For one thing, you don't tend to get any photos with you in them when hiking alone! :-)

And I don't think that hiking alone is inherently dangerous. Sometimes group dynamics are such that the group is collectively smarter than any individual in it. And sometimes it's the reverse, the group as a whole is dumber than the average IQ of the group as a whole. In the latter case, hiking solo can be safer than hiking with the group.

In any event, it sure is nice to take breaks exactly when you want them, for exactly as long as you want, to make camp whenever you feel like it, to walk the pace that you want to walk, all without consulting or compromising.