Unexpected behaviour
Hello !
I discovered an unexpected behaviour while using pandas

## Code Sample
```
import pandas as pd

def process(df):
	df.index = df["A"]
	df.loc['first', 'A'] = 'first'

	print("Before")
	print(df)
	print()

	df.loc['first', 'B'] = 99

	print("After")
	print(df)


print("First processing : without csv file :\n")

df = pd.DataFrame({'A': ["first", "second"], 'B': [3,4]})
process(df)

print("\n\nSecond processing : via a csv file :\n")

df = pd.DataFrame({'A': ["first", "second"], 'B': [3,4]})
df.to_csv("df.csv",index=False)
df = pd.read_csv("df.csv")
process(df)
```
## Problem description
The 2 output that `process(df)` produces are different if `df` have been previously exported to a csv file or not.

## Expected output
```
First processing : without csv file :

Before
             A  B
A                
first    first  3
second  second  4

After
             A   B
A                 
first    first  99
second  second   4


Second processing : via a csv file :

Before
             A  B
A                
first    first  3
second  second  4

After
             A  B
A                   
first    first  99
second  second   4
```
## Actual output
```
First processing : without csv file :

Before
             A  B
A                
first    first  3
second  second  4

After
             A   B
A                 
first    first  99
second  second   4


Second processing : via a csv file :

Before
             A  B
A                
first    first  3
second  second  4

After
             A     B
A                   
first      NaN  99.0
second  second   4.0
first      NaN  99.0
```
## Mea culpa
I guess that writing `df.index = df["A"]` is a bad practice because comumn `A` is still linked to the index. So when we modify column `A`, the index is changed as well. It could be good to raise a Warning to tell silly people like me that I shouldn't do that.

Thank you, and have a cute day !

[show_versions.txt](https://github.com/pandas-dev/pandas/files/4677020/show_versions.txt)
