How do you forget to lubricate a chain after cleaning? If this is a possibility, you a would be better not to clean the chain at all.
White spirit is a generic name for different products, exactly what it means depends where in the world you live. Some have a flash point of 20–30°C — extreme care is needed using it. Others with higher flash points and lower volatility are safer (but not entirely safe). All are hydrocarbon based and environmentally unfriendly if disposed of improperly. Care should be taken using them
To understand the arguments of what cleaner is best, you need to understand chains.
New chains come factory lubed with a very robust and long lasting lube that is much better than anything you can apply. The last thing you want to do is use a cleaner that will strip this lube off the chain, in fact, for the first few hundred kilometers no cleaning is probably best. White spirit is one of those cleaners. Once the chain is older, and this lube is worn off, it needs replacing. Stripping the replacement lube off completely is not problem — it's easy to lube the chain and get the same level of lubrication as you had.
So should you use it on new chains? No way. On old chains, it won't matter. Question is when does new become old? Who knows. Easy answer and most (profitable for bike shop) is use a dedicated bike chain cleaner (you buy from them).
In the end I don't think it matters, as long as you are cleaning the chain regularly and lubing it properly.
There are plenty of questions on this site and discussions on the internet about the various religions of chain maintenance you can delve into if you desire.