We have the right to strike because we live in a democracy. As citizens in a democracy, we have a say in the way our society is run and when negotiations take place, to which the outcome would be detrimental, we have a right to express our opinions peacefully, maybe through a strike, or hopefully long before that, many other forms of civil action. When you cross a picket line, you undermine the collective action of everyone else who is fighting for their rights.
We have a voice and therefore we have a right to strike. Should you wish to not have a voice, you can chose to not participate, to not vote, to not strike etc. However, trade unions are the reason why fewer people die at work, why employment laws protect us, why women have equal pay legislation (even though there's still a great deal of work still needed to make that a true reality.
The UK spends a smaller proportion of its GDP on wages now, than it ever has before. There are strikes because the money that we earn is worth less now than it was 10 years ago, living expenses are higher and employees are being squeezed tighter and tighter.