bash: set -o errexit is not exiting when a command has an error. how do you change code to make it exit when there is an error?

Question

here is the minimal code (tested on centos7 bash 4.2 and rocky8 bash 4.4):

#!/bin/bash

func1() {
    echo a
    echo b
    cd asdfasdf123
    echo "c: should not get here"
    echo "d: should not get here"
}

main() {
    echo "DEBUG: $FUNCNAME: LINENO=$LINENO"

    exitcode=0
    func1 || exitcode=1

    echo "DEBUG: $FUNCNAME: LINENO=$LINENO"

    func1

    echo "DEBUG: $FUNCNAME: LINENO=$LINENO"
}

set -x
set -eu
main

• in the first call of func1: i am expecting the code to never print the echo c line of code. but instead i see that the code does get to the echo c line of code.
• in the second call of func1: i see that the code does correctly exit when the error happens.

this is bad because i have a larger important shell program that gets an error early in the code and does not exit when i need the code to exit and instead keeps going even though the early operation did not do what i needed it to do.

set -o errexit is not exiting when a command has an error. how do you change this code to make it exit when there is an error?