I think it's generally the older generation who seem to think solo travel is weird. I had a similar reaction whilst I was sat on the plane flying out to Germany on my own after I broke up with my partner. We had a trip to Berlin already booked but as it was somewhere I'd always wanted to go I decided to just go on my own anyway and I'm so glad I didn't cancel because it was the best decision ever.
I stayed in a hostel and met loads of interesting people, some of whom I still message occasionally on Facebook now and no doubt will meetup with again in the future. Being thrown in to a different environment / culture on your own not knowing anyone in the country was actually quite an adrenaline rush I found. I had to navigate public transport, read maps to get to places and try and understand various signs in a foreign language whilst attempting to speak the language at times, it was all part of the fun. Also as someone else mentioned the freedom to not be tied to anyone's schedule other than your own is a great feeling and shouldn't be underestimated. You can plan your own itinerary and change it as and when you want which gives a great sense of freedom. I think the only time when I became a little apprehensive was the first night when I arrived and was sat in the bar on my own thinking what if I don't talk to anyone or meet anyone and felt a tiny bit lonely but after a couple of drinks I had the dutch courage to strike up conversations with random people and that's how I ended up meeting so many awesome people.
I'm planning my next solo adventures already and can't wait. If you apply common sense you are often fine and for the most part people are generally helpful and kind, despite how bleak the world appears at times.
