Today, it's hard to see the big deal about the GOTO statement because the "structured programming" people mostly won the debate and today's languages have sufficient control flow structures to avoid GOTO.
Count the number of gotos in a modern C program. Now add the number of break, continue, and return statements. Furthermore, add the number of times you use if, else, while, switch or case. That's about how many GOTOs your program would have had if you were writing in FORTRAN or BASIC in 1968 when Dijkstra wrote his letter.
Programming languages at the time were lacking in control flow. For example, in the original Dartmouth BASIC:
IF statements had no ELSE. If you wanted one, you had to write:
100 IF NOT condition THEN GOTO 200
...stuff to do if condition is true...
190 GOTO 300
200 REM else
...stuff to do if condition is false...
300 REM end if
Even if your IF statement didn't need an ELSE, it was still limited to a single line, which usually consisted of a GOTO.
There was no DO...LOOP statement. For non-FOR loops, you had to end the loop with an explicit GOTO or IF...GOTO back to the beginning.
There was no SELECT CASE. You had to use ON...GOTO.
So, you ended up with a lot of GOTOs in your program. And you couldn't depend on the restriction of GOTOs to within a single subroutine (because GOSUB...RETURN was such a weak concept of subroutines), so these GOTOs could go anywhere. Obviously, this made control flow hard to follow.
This is where the anti-GOTO movement came from.
