BUG: pandas read_csv silently switches date parsing scheme in the middle of reading file corrupting data
In pandas 1.1.4

```python
# Your code here
pd.DataFrame(data={'timestamp':  ['13/06/2018', '12/06/2018']}).to_csv('test.csv', index=False)
pd.read_csv('test.csv', parse_dates=['timestamp'])

Out[84]: 
   timestamp
0 2018-06-13
1 2018-12-06
```

#### Problem description

I provoked pandas here (initially by mistake) by letting it parse a file with date format day / month / year, with it's default parser month / day / year. To my horror, it parses the ones that give a valid date with the default parser, and automatically uses the alternative parser on the ones that fails. Giving a mix of dates and without any warning. 

#### Expected Output
Pandas should have failed with an error, or a very severe warning when a date failed to parse with the same parser as the other dates. It should not be allowed to use different parsing schemes within the same data file.

<details>

pandas           : 1.1.4
numpy            : 1.19.4
pytz             : 2020.4
dateutil         : 2.8.1

</details>
