It may be because you are in a protected zone on a server or you could be in adventure mode. Sometimes there is also block lag which can even happen on singleplayer.
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You can always break and build any thing u want in creative. If you are in "adventurer mode" that stops you from braking and placing blocks.
Some blocks require certain tools, while most can be broken unarmed. Just left-click and hold to break blocks and right-click to place blocks.
Adventure maps are usually used in minecraft maps it allows you to not break certain blocks but you can use a certain item to break that block.
You need a Diamond Pick to harvest obsidian blocks.
Minecraft characters are approximately 2 blocks high.