Tony, Brian,
Thank you very much for your answers.
I had no idea that birch was a difficult wood to turn: I fell a birch tree in my garden, made a lathe from it and simply used an off-cut as a first try. I discovered that the wood was spalted while axing away the rough bowl.
As you both suggested, the spalting was indeed not helpful to me as a beginner. On close inspection, the tear out occurred mostly in the spalted regions.
I eventually managed to turn a bowl reasonably free of tear out although the shape was more dictated by the recovery of the successive catches/dig-ins than my own will...



The things I found helpful in reducing tearout were:
- Using the smallest possible gouge that I had (8mm) and striving for the lightest cuts as manageable. Anything bigger than this gouge apparently was too aggressive to the frail spalted areas and tore off chunks of wood no matter how sharp the tools. I tried to use the skew chisel but the catches forced me to remove about 4mm in radius each time so I eventually gave up.
- Sharpening the gouge VERY often. I would typically sharpen the gouge, work for 2 minutes, strop the tool, work for 2 minutes, strop the tool, work for 2 minutes and sharpen the tool afresh. All in all, a pretty time consuming way to work and I probably spent nearly as much time sharpening as turning... I feel that I ended up sharpening more to compensate for my lack of technique. I am left wondering when I read tutorials online mentioning that the hooks need not be razor sharp...
I left the surface as it was cut from the tool and dud not try to sand away the mistakes (merely burnished the surface with wood shavings) as I would like to be able to compare this first bowl to the next ones and see if my technique improves. The 2 last pictures were taken after I coated the bowl with some walnut oil.
Brian, I understand what you mean regarding the difficulty to hollow out the bowl without hooks. I felt that my gouge would only allow me so much angle and I was not able to match exactly the same curve on the inside than on the outside.
Anyway, it was still a nice project, thank you once again for your help.