Repointing is often under respected. 

It is absolutely vital to the health of a building and can very easily cause more problems than it solves. If I had to choose one thing that causes the most damage to historic masonry it would be amateur repointing.  When you undertake plastering for instance an awful lot of the issues can be mitigated by the other improvements which often take place, such as improved ventilation or good paint. I should however stress that internal repointing is much less likely to cause problems, but on the other hand unless you live in a bloody Medieval Castle its likely that no masonry was ever exposed, ergo no repointing required. Please stop doing things to old properties because of current trends, it kind of defeats the object of living in a timeless structure or building when you alter it every generation... 

The reasons for using lime;

Matches expansion and contraction rates of the original. 

Dries out masonry. 

Autogenously repairs.

Absorbs harmful substances which damage the building like salts,

Bullshit reasons; Don't like how it looks, Keeping up with the Jones. Lime is best for everything. Someone in a shop said I should. Its the only answer amateurs have to the restoration of older properties.  

The reasons for repointing;

Its not there...

It has been compromised and lets in water.

Its full of salt, been subject to mineralization and therefore unbreathable, possibly even attracting water to it. Common internally at wall bases where the original floor has been replaced by concrete. 

Its been done wrong previously.

To mitigate damage to historic masonry, this list is long and tedious. 

Before you specify your mortar you must determine the lime content of the original, one way or another. If you don't then the original mortar may well have a stronger capillary action than the new mortar resulting in it trapping water. This is what peope describe as hard mortar, impermeable mortar etc. Its not, its just got incredibly low suction in comparison to the original mortar behind it. So looks like its trapping water. Perversely the original lime mortar is the one trapping water. This problem is worse with the presence of hygroscopic salts in the original mortar. 

Hardness of mortar affecting masonry is manifested in cracking of the building units and delamination of the pointing from the aforementioned. The reason for this is that the bulk of the wall is moving a lot in comparison to the repointed face and the mortar, as a mesh, can be stronger than the faxce of the stone or brick, which is often compromised. It is not easy to make a mortar which is actually stronger than brick or stone on its own. Its the mesh vs an individually building unit that cause the problem and the difference in overall strength of the masonry, not one mortar vs the other. Hence why a mortar like NHL 3,5, which is 3,5N can damage building stone which has a strength of 20N+. imagine throwing a strong net over a load of lumps and some of them are weaker than the other, they will break first and the collective strength of that action is greater than its constituent parts. I suspect engineers are cringing at my poor description of this, sorry. 

The next consideration is whether you can improve on what was originally there. We have the knowledge and skills to improve upon our historic counterparts and they often got things wrong. We also live in completely different conditions now, so both externally and internally the environment is different to when the original mortar was specified. We live hotter and sweatier internally and pollute more externally. 

Now we want to determine the ratio of water ingress and egress, the amount of water we allow to penetrate the mortar and how much it can convect off. This is important in exposure zones with a higher rating, It is also something which is woefully ignored. One can make a lime mortar which is resistant to erosion without resorting to turing it up to elevem, sorry making it hydraulic. This is determined and controlled through the use of bio and mineral additives. Also the method and material for finishing that is used to tool up the mortar. Beating back with a brush allows the most water ingress and steel the least with a range of materials and methods inbewteen the two. steel is also problematic for other reasons.

The next consideration is how much crap it needs to manage, salt, pollution etc. This is very specific and often determined through observation and even testing of the existing mortar. The materials used and how you apply and finish them are the methods of control for this. 

The type of building unit is next, it has to be compatible to that. Historically some mortars weren't so this can be tricky. You may have to compromise in some way to ensure compatibility between the existing mortar and your preferred specification. 

https://mortar.org.uk/documents/MPA-Mortar-Data-Sheet-19.pdf

https://mortar.org.uk/documents/MPA-Mortar-Data-Sheet-21.pdf

How to repoint;

Lol, its not that simple. but I may put up some pointers and a rough guide at some point.