Why does Sql Server keep executing after raiserror when xact_abort is on?

This is By Design^TM, as you can see on Connect by the SQL Server team's response to a similar question:

Thank you for your feedback. By design, the XACT_ABORT set option does not impact the behavior of the RAISERROR statement. We will consider your feedback to modify this behavior for a future release of SQL Server.

Yes, this is a bit of an issue for some who hoped RAISERROR with a high severity (like 16) would be the same as an SQL execution error - it's not.

Your workaround is just about what you need to do, and using an explicit transaction doesn't have any effect on the behavior you want to change.

If you use a try/catch block a raiserror error number with severity 11-19 will cause execution to jump to the catch block.

Any severity above 16 is a system error. To demonstrate the following code sets up a try/catch block and executes a stored procedure that we assume will fail:

assume we have a table [dbo].[Errors] to hold errors assume we have a stored procedure [dbo].[AssumeThisFails] which will fail when we execute it

-- first lets build a temporary table to hold errors
if (object_id('tempdb..#RAISERRORS') is null)
 create table #RAISERRORS (ErrorNumber int, ErrorMessage varchar(400), ErrorSeverity int, ErrorState int, ErrorLine int, ErrorProcedure varchar(128));

-- this will determine if the transaction level of the query to programatically determine if we need to begin a new transaction or create a save point to rollback to
declare @tc as int;
set @tc = @@trancount;
if (@tc = 0)
 begin transaction;
else
 save transaction myTransaction;

-- the code in the try block will be executed
begin try
 declare @return_value = '0';
 set @return_value = '0';
 declare
  @ErrorNumber as int,
  @ErrorMessage as varchar(400),
  @ErrorSeverity as int,
  @ErrorState as int,
  @ErrorLine as int,
  @ErrorProcedure as varchar(128);


 -- assume that this procedure fails...
 exec @return_value = [dbo].[AssumeThisFails]
 if (@return_value <> 0)
  raiserror('This is my error message', 17, 1);

 -- the error severity of 17 will be considered a system error execution of this query will skip the following statements and resume at the begin catch block
 if (@tc = 0)
  commit transaction;
 return(0);
end try


-- the code in the catch block will be executed on raiserror("message", 17, 1)
begin catch
  select
   @ErrorNumber = ERROR_NUMBER(),
   @ErrorMessage = ERROR_MESSAGE(),
   @ErrorSeverity = ERROR_SEVERITY(),
   @ErrorState = ERROR_STATE(),
   @ErrorLine = ERROR_LINE(),
   @ErrorProcedure = ERROR_PROCEDURE();

  insert #RAISERRORS (ErrorNumber, ErrorMessage, ErrorSeverity, ErrorState, ErrorLine, ErrorProcedure)
   values (@ErrorNumber, @ErrorMessage, @ErrorSeverity, @ErrorState, @ErrorLine, @ErrorProcedure);

  -- if i started the transaction
  if (@tc = 0)
  begin
   if (XACT_STATE() <> 0)
   begin
     select * from #RAISERRORS;
    rollback transaction;
    insert into [dbo].[Errors] (ErrorNumber, ErrorMessage, ErrorSeverity, ErrorState, ErrorLine, ErrorProcedure)
     select * from #RAISERRORS;
    insert [dbo].[Errors] (ErrorNumber, ErrorMessage, ErrorSeverity, ErrorState, ErrorLine, ErrorProcedure)
     values (@ErrorNumber, @ErrorMessage, @ErrorSeverity, @ErrorState, @ErrorLine, @ErrorProcedure);
    return(1);
   end
  end
  -- if i didn't start the transaction
  if (XACT_STATE() = 1)
  begin
   rollback transaction myTransaction;
   if (object_id('tempdb..#RAISERRORS') is not null)
    insert #RAISERRORS (ErrorNumber, ErrorMessage, ErrorSeverity, ErrorState, ErrorLine, ErrorProcedure)
     values (@ErrorNumber, @ErrorMessage, @ErrorSeverity, @ErrorState, @ErrorLine, @ErrorProcedure);
   else
    raiserror(@ErrorMessage, @ErrorSeverity, @ErrorState);
   return(2); 
  end
  else if (XACT_STATE() = -1)
  begin
   rollback transaction;
   if (object_id('tempdb..#RAISERRORS') is not null)
    insert #RAISERRORS (ErrorNumber, ErrorMessage, ErrorSeverity, ErrorState, ErrorLine, ErrorProcedure)
     values (@ErrorNumber, @ErrorMessage, @ErrorSeverity, @ErrorState, @ErrorLine, @ErrorProcedure);
   else
    raiserror(@ErrorMessage, @ErrorSeverity, @ErrorState);
   return(3);
  end
 end catch
end

Use RETURN immediately after RAISERROR() and it'll not execute the procedure further.

As pointed out on the docs for SET XACT_ABORT, the THROW statement should be used instead of RAISERROR.

The two behave slightly differently. But when XACT_ABORT is set to ON, then you should always use the THROW command.