The point about teachers not getting paid for strikes is that this means effectively they are fined for unauthorized term time absence, just like parents. The govt fines us all for unauthorized term time absence so there is no inequality there.
The government don't want kids out on holiday. They also don't want teachers to strike. They don't want children's education to be disrupted. There is no inconsistency between strike action and fines on term time holidays.
Therefore, the opening post is flawed, illogical and very wrong.
Unions are very important as previously explained to prevent the exploitation of workers and they are responsible for the employment laws we all benefit from today in terms of paid holiday, rights, parental leave etc. If throughout history, employees had always attempted to 'talk not walk' you wouldn't be able to take your kids on holiday in the first place because you would have no employee rights to have that time off yourself.
People accuse striking teachers of being selfish. They are selfish as their objections are based solely on the inconvenience of having to organise their own childcare for one day and they can't be bothered to find out about the issues affecting education now and the long-term threat to the quality of their own children's education if teachers do not protest about the changes being proposed.
It's also not selfish to strike about pay and pensions - if these are eroded, this will have a severe impact on the number and quality of people entering the teaching profession. I want my children to have a high quality education - teachers are striking in an attempt to preserve this. Decent pay and pensions is one way to attract and retain good staff.