C# .NET Stream.BeginRead() is blocking, not parallel thread

// aioee.cs - Testing Asynchronous I/O  -  EE ask version
 
using System;
using System.IO;
using System.Text;
using System.Threading;
 
namespace AIOEE
{
	public class AsyncTest
	{
		// private const int bufferSize = 10;           // to try to slow it down
		private const int bufferSize = 256;             // arbitrary
		// private const int bufferSize = 4000;         // suggested by djon2003
		// private const int bufferSize = 1000000000;   // fast, of course
		
		private const string inputFileName = "somefile.txt";
		
		private byte[] buffer;
		private Stream inStream;
		private AsyncCallback callbackMethod;
		
		public AsyncTest()
		{
			inStream = File.OpenRead(inputFileName);
			buffer = new byte[bufferSize];
			callbackMethod = new AsyncCallback(this.OnCompletedRead);
		}  // end AsyncTest()  ctor
		
		public static void Main(string[] args)
		{
			AsyncTest tester = new AsyncTest();
			tester.Run();
			
		} // end Main()
		
		public void Run(string[] args)
		{
			// using null instead of a local state object
			inStream.BeginRead(buffer, 0, buffer.Length, callbackMethod, null);
			Console.WriteLine("Run():  Immediately following BeginRead() call.");
			
			// do some token work in between to prove that we're asynchronous.
			// Note that this never shows up until the end regardless of file/buffer sizes,
			// which means the BeginRead() is blocking.
			for (long i=0; i<=100000; i++)
			{
				if (i%1000 == 0)
				{
					Console.WriteLine("i:  {0}", i);
				}  // end if
			
			}  // end for
			
		} // end Run()
		
		
		// Callback method.
		void OnCompletedRead(IAsyncResult asyncResult)
		{
			Console.WriteLine("HIT ONCOMPLETEDREAD Method.");
			
			int bytesRead = inStream.EndRead(asyncResult);
			
			if (bytesRead == 0)
			{
				Console.WriteLine("OnCompletedRead():  No bytes read -- must be done");
			}
			else
			{
				string s = Encoding.ASCII.GetString(buffer, 0, bytesRead);
				
				// my this could get large
				// Console.WriteLine(s);
				
				// If bytes have been read, try to read more
				// Is this why I'm blocking?
				// Is this also why I'm bombing on large files with small buffer sizes?
				inStream.BeginRead(buffer, 0, buffer.Length, callbackMethod, null);
				
			}  // end if-else
			
		}  // end OnCompletedRead()
		
	}  // end class AsyncTest
	
} // end namespace AIOEE
                                              

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void Run()
{
   // ...
                                              

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