BUG: DatetimeIndex.intersection gives incorrect result
- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
import pandas as pd
index = pd.DatetimeIndex(['2018-12-31', '2019-03-31', '2019-06-30', '2019-09-30', '2019-12-31', '2020-03-31'], freq='Q-DEC')
print(index[::2].intersection(index[1::2]))
```

#### Problem description

The produced output is:
DatetimeIndex(['2019-06-30', '2019-12-31'], dtype='datetime64[ns]', freq='2Q-DEC')

This is clearly incorrect, as there is no overlap between the indices index[::2] and index[1::2].

The issue is related to the freq attribute, which is set to '2Q-DEC' for both index[::2] and index[1::2]. If I remove or change the freq attribute, then it works correctly.

#### Expected Output

DatetimeIndex([], dtype='datetime64[ns]', freq=None)

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 2cb96529396d93b46abab7bbc73a208e708c642e
python           : 3.8.5.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 20.5.0
Version          : Darwin Kernel Version 20.5.0: Sat May  8 05:10:33 PDT 2021; root:xnu-7195.121.3~9/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : en_US.UTF-8
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.2.4
numpy            : 1.20.3
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.0.1
setuptools       : 52.0.0
Cython           : 0.29.17
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : 0.4.1
xlsxwriter       : 1.4.3
lxml.etree       : 4.6.3
html5lib         : None
pymysql          : None
psycopg2         : 2.8.6 (dt dec pq3 ext lo64)
jinja2           : None
IPython          : 7.21.0
pandas_datareader: 0.9.0
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.4
numexpr          : None
odfpy            : None
openpyxl         : 3.0.6
pandas_gbq       : None
pyarrow          : 3.0.0
pyxlsb           : None
s3fs             : None
scipy            : 1.4.1
sqlalchemy       : 1.3.23
tables           : None
tabulate         : 0.8.9
xarray           : None
xlrd             : None
xlwt             : 1.3.0
numba            : 0.52.0

</details>
