Why disposing StreamReader makes a stream unreadable?

I need to read a stream two times, from start to end.

But the following code throws an ObjectDisposedException: Cannot access a closed file exception.

string fileToReadPath = @"<path here>";
using (FileStream fs = new FileStream(fileToReadPath, FileMode.Open))
{
    using (StreamReader reader = new StreamReader(fs))
    {
        string text = reader.ReadToEnd();
        Console.WriteLine(text);
    }

    fs.Seek(0, SeekOrigin.Begin); // ObjectDisposedException thrown.

    using (StreamReader reader = new StreamReader(fs))
    {
        string text = reader.ReadToEnd();
        Console.WriteLine(text);
    }
}

Why is it happening? What is really disposed? And why manipulating StreamReader affects the associated stream in this way? Isn't it logical to expect that a seekable stream can be read several times, including by several StreamReaders?