Is Task always decomposed from User Story?
Tasks are often split from a user story, but that does not mean that a task can only exist as part of user stories and thus they always have a smaller size. Tasks can exist by themselves.
You tagged the question Scrum. User stories are not a Scrum specific thing. Your Product Backlog isn't composed of user stories only. You can have epics, stories, bugs, tasks, spikes, or whatever your product needs. Scrum generically calls all of these Product Backlog Items.
When working with user stories, some teams prefer to split them into tasks, but that's not mandatory, it's a preference. Sometimes it's even problematic because they can split the story horizontally in things like "build the database queries", "build the back-end", "build the front-end", "code review", "testing" etc, which can create development silos inside the team instead of everyone finding a way to collaborate on the story while at the same time finding the right balance to work individually. I for example don't like splitting stories into tasks. Some argue that tasks allow you to see progress better within the sprint, and your burn down chart looks better, but I don't find that useful because if you have a story split into 5 tasks, if you only finish 4 of them the story is not done either way. But I digress...
Getting back to the task being larger than a story, yes it's possible. Like I said, a task can be a product backlog item just like a user story can be. You could have some technical tasks in the backlog that are larger than some stories.
Say you have a story for doing login. The team might finish that in half a day. But they also have a technical task to update the framework libraries and some of its methods were deprecated in between versions. Now the team needs to make small changes here and there and that takes them the entire day. The framework task in this example is twice as large as the login user story.