Python CSV not writing data to file - python-3.x

Question

I am running into a wall with this. I am new to writing CSV files with python and have been reading lots of different posts on the topic, but now I ran into a wall with this and could use a little help.
import csv
#headers from the read.csv file that I wan't to parse and write to the new file.
headers = ['header1', 'header5', 'header6', 'header7']
#open the write.csv file to write the data to
with open("write.csv", 'wb') as csvWriter:
writer = csv.writer(csvWriter)
#open the main data file that I want to parse data out of and write to write.csv
with open('reading.csv') as csvfile:
readCSV = csv.reader(csvfile, delimiter=',' )
csvList = list(readCSV)
#finds where the position of the data I want to pull out and write to write.csv
itemCode = csvList[0].index(headers[0])
vendorName = csvList[0].index(headers[1])
supplierID = csvList[0].index(headers[2])
supplierItemCode = csvList[0].index(headers[3])
for row in readCSV:
writer.writerow([row[itemCode], row[vendorName], row[supplierID], row[supplierItemCode]])
csvWriter.close()
---UPDATE---
I made the changes suggested and tried commenting out the following part of the code & changing 'wb' to 'w' and the program worked. However, I don't understand why, and how do I set this up so that I can list the header I want to pull out?
csvList = list(readCSV)
itemCode = csvList[0].index(headers[0])
vendorName = csvList[0].index(headers[1])
supplierID = csvList[0].index(headers[2])
supplierItemCode = csvList[0].index(headers[3])
Here is my updated code:
headers = ['header1', 'header5', 'header6', 'header7']
#open the write.csv file to write the data to
with open("write.csv", 'wb') as csvWriter, open('reading.csv') as csvfile:
writer = csv.writer(csvWriter)
readCSV = csv.reader(csvfile, delimiter=',' )
"""csvList = list(readCSV)
#finds where the position of the data I want to pull out and write to write.csv
itemCode = csvList[0].index(headers[0])
vendorName = csvList[0].index(headers[1])
supplierID = csvList[0].index(headers[2])
supplierItemCode = csvList[0].index(headers[3])"""
for row in readCSV:
writer.writerow([row[0], row[27], row[28], row[29]])

Answer 1

It looks like you want to write a subset of columns to a new file. This problem is simpler with DictReader/DictWriter. Note the correct use of open when using Python 3.x. Your attempt was using the Python 2.x way.
import csv
# headers you want in the order you want
headers = ['header1','header5','header6','header7']
with open('write.csv','w',newline='') as csvWriter,open('read.csv',newline='') as csvfile:
writer = csv.DictWriter(csvWriter,fieldnames=headers,extrasaction='ignore')
readCSV = csv.DictReader(csvfile)
writer.writeheader()
for row in readCSV:
writer.writerow(row)
Test data:
header1,header2,header3,header4,header5,header6,header7
1,2,3,4,5,6,7
11,22,33,44,55,66,77
Output:
header1,header5,header6,header7
1,5,6,7
11,55,66,77

Answer 2

if you want to access both writer under the same block,you should do something like this
with open("write.csv", 'wb') as csvWriter,open('reading.csv') as csvfile:
writer = csv.writer(csvWriter)
readCSV = csv.reader(csvfile, delimiter=',' )
csvList = list(readCSV)
#finds where the position of the data I want to pull out and write to write.csv
itemCode = csvList[0].index(headers[0])
vendorName = csvList[0].index(headers[1])
supplierID = csvList[0].index(headers[2])
supplierItemCode = csvList[0].index(headers[3])
for row in readCSV:
writer.writerow([row[itemCode], row[vendorName], row[supplierID], row[supplierItemCode]])
csvWriter.close()

Answer 3

The with open() as csvWriter: construct handles closing of the supplied file once you exit the block. So once you get down to writer.writerow, the file is already closed.
You need to enclose the entire expression in the with open block.
with open("write.csv", 'wb') as csvWriter:
....
#Do all writing within this block
....